Algebra Calculator

Type one equation, pick the letter, click Calculate. This algebra calculator solves whatever sits in the box, instantly and right on the page.

• Equation (one = sign) — any equation with a single unknown. The box comes preloaded with $3(x - 2) = 12$; press Calculate and the algebra calculator answers $x = 6$. Linear equations, brackets, fractions such as $5x/2 + 1 = 4$, and quadratics such as $x^2 - 9 = 0$ all work.
• Solve for — the letter you are hunting. Leave it on x for most homework; switch to y, z, t, or n when the equation uses a different letter.
• Press Calculate and the solution comes back in one line — $x = 6$ for the preloaded equation — solved the same way every example below is solved by hand.

The algebra calculator handles the rearranging and the arithmetic; the rest of this page opens the box and shows every move slowly.

This page is more than a static algebra calculator — it is also an AI tutor you can ask questions:

• Ask in plain words. “Twice a number plus three gives seven — what is the number?” The AI turns the sentence into $2x + 3 = 7$ and solves it step by step.
• Take a photo of your homework. No typing: the AI reads the equation straight off the page and solves it step by step.
• Ask about the ideas, not just the number. “Why do we add 6 to both sides?” The AI explains the move — and you can check every number against the algebra calculator on this page, so nothing is guessed.
• Work backwards, then keep asking. Give the AI a word problem to turn into an equation, or an answer and ask for the equation behind it. Follow-ups are welcome, so ask “why?” as often as you need: this algebra calculator page keeps teaching.

Algebra begins with one small move: replace the unknown number with a letter. Instead of “some number that, when doubled and increased by 3, gives 7,” you write $2x + 3 = 7$. The letter $x$ holds the seat of a number you do not know yet, and the equation becomes a question you can answer with moves instead of guessing.

Every equation is also a balance scale. The = sign is the pivot; the two sides weigh the same. Picture $3(x - 2)$ on the left pan and $12$ on the right:

$3(x - 2) = 12$

Remove something from one pan and the scale tips — unless you remove the same thing from the other pan too. That single picture powers every move an algebra calculator makes: whatever you do to one side, do to the other, and the equality survives. Solving is a sequence of legal moves that leaves the letter alone on one pan and a number on the other.

This is why algebra is worth learning even with an algebra calculator on the page: the tool makes the moves at speed, but the balance picture is what tells you whether a move is legal at all. The rest of this page walks those moves slowly — brackets, squares, and letters on both sides included.

The balance method is the whole toolkit for solving equations. Four legal moves exist, and each one keeps the scale level:

One habit falls out of the table, and it is the one teachers watch for: moving a term across the = sign flips its sign. Subtracting 6 from both sides of $3x - 6 = 12$ is the same as letting the $-6$ cross the pivot and land as $+6$ on the right: $3x = 12 + 6$. The sign flip is not a new rule — it is subtraction viewed from the far side of the scale.

Play the moves in order — clear brackets, collect the letters on one side, strip the constants, divide out the coefficient — and any equation shrinks to $x = \text{number}$. The algebra calculator above runs exactly this sequence; the three examples below walk it by hand.

Solve $3(x - 2) = 12$ — the equation preloaded in the algebra calculator above.

1. Expand the brackets: $3(x - 2) = 3x - 6$, so the equation reads $3x - 6 = 12$.
2. Add 6 to both sides: $3x = 12 + 6 = 18$.
3. Divide both sides by 3: $x = 18 \div 3 = 6$.
4. Check by substituting: $3(6 - 2) = 3 \times 4 = 12$. Both sides agree, so $x = 6$ is the solution.

There is a second, faster route worth seeing: divide both sides by 3 first, which gives $x - 2 = 4$, then add 2 to land on $x = 6$ — the same answer by a shorter path. Two legal routes, one solution: that is normal in algebra, and it is why checking the answer matters more than admiring the route.

Type $3(x - 2) = 12$ into the algebra calculator above and it returns $x = 6$ in one click. The four hand steps are the same moves the algebra calculator makes — expand, strip the constant, divide, check — just slow enough to copy into a notebook.

Solve $x^2 - 9 = 0$. A square changes the game: there can be two answers, and this one has exactly two.

1. Recognize the difference of squares: $x^2 - 9 = (x - 3)(x + 3)$.
2. Apply the zero product property: if $(x - 3)(x + 3) = 0$, then $x - 3 = 0$ or $x + 3 = 0$ — a product can be zero only through one of its factors.
3. Solve each small equation: $x = 3$ or $x = -3$.
4. Check both: $3^2 - 9 = 0$ and $(-3)^2 - 9 = 9 - 9 = 0$. Both work.

So the full answer is $x = 3$ or $x = -3$. Reporting only one of them is the classic half-answer — both roots belong in the final line.

The algebra calculator handles this input as-is: type $x^2 - 9 = 0$ and both roots come back together, because the solver factors rather than guesses. When a square appears in your homework, pause before circling the first root and ask whether a second is waiting. For quadratics that refuse to factor, the quadratic formula calculator page on this site gives the method that always works.

Solve $5x = 2x + 6$. The letter now sits on both sides of the pivot, which looks harder than it is. The routine does not change — collect the letters first.

1. Subtract $2x$ from both sides so every $x$ lands on the left: $5x - 2x = 6$, so $3x = 6$.
2. Divide both sides by 3: $x = 2$.
3. Check both originals: $5(2) = 10$ and $2(2) + 6 = 10$. The two sides match, so $x = 2$ is the solution.

The order matters. Had you divided by 5 first, the $2x$ would ride along into fraction territory and the tidying would only get longer. Gathering the letters onto one side before anything else is almost always the cheaper first move, and it is the one the algebra calculator makes on inputs of this shape.

Two habits survive every equation on this page: collect before you divide, and substitute the answer back in before writing it on the homework line. The algebra calculator above runs both habits on every input, including this one.

Three slips the algebra calculator catches every day. In each one the tool stays right and the handwriting goes wrong:

1. Moving a term without flipping its sign. From $3x - 6 = 12$, the $-6$ that crosses the = sign lands as $+6$: $3x = 18$. Let it cross as $-6$ and you get $3x = 6$ — a tidy-looking wrong answer. Slow down at every minus sign; that is where most lost marks live.
2. Dividing both sides by an expression that contains the unknown. Dividing by a plain number is legal; dividing by something with $x$ in it can throw away a solution, because any value that makes the divisor zero quietly vanishes from the answer. Move everything to one side and factor instead — that is what the algebra calculator does internally, and it never loses a root this way.
3. Distributing to only one term inside the brackets. $3(x - 2)$ means 3 times the $x$ and 3 times the 2: $3x - 6$, never $3x - 2$. Miss the second multiplication and every later line inherits the error.

One habit prevents all three: substitute your answer into the original equation before circling it. If the two sides do not match, the algebra calculator will not match you either.