Type any equation and get a clear, step-by-step solution in seconds. Our free equation solver handles linear, quadratic, and many other equations, showing the work so you actually learn how the answer is found.
Free · Step-by-step worked solutions · Works on any device
What this equation solver does
This equation solver takes an equation you type in and finds the value (or values) of the unknown that make it true. Instead of just handing you a final number, it walks through each step so you can see exactly how the solution comes together.
It is built to handle a wide range of problems, including:
- Linear equations like \( 3x + 7 = 22 \) and equations with variables on both sides.
- Quadratic equations such as \( x^2 - 5x + 6 = 0 \), solved by factoring or the quadratic formula.
- Equations with fractions, parentheses, and like terms that need simplifying first.
- Problems where you need to solve for a specific variable, even when there are several letters.
Just enter the equation using the keyboard or the built-in equation editor, and our AI engine returns a complete, readable worked solution.
Worked examples
Example 1: A linear equation
Solve \( 3x + 7 = 22 \).
Subtract 7 from both sides to isolate the \( x \) term:
$$ 3x + 7 - 7 = 22 - 7 \quad\Rightarrow\quad 3x = 15 $$Divide both sides by 3:
$$ x = \frac{15}{3} = 5 $$Check: \( 3(5) + 7 = 15 + 7 = 22 \). It works.
Example 2: Variables on both sides
Solve \( 5(x - 2) = 3x + 4 \).
First distribute the 5 on the left:
$$ 5x - 10 = 3x + 4 $$Subtract \( 3x \) from both sides to gather the variables together:
$$ 2x - 10 = 4 $$Add 10 to both sides, then divide by 2:
$$ 2x = 14 \quad\Rightarrow\quad x = 7 $$Check: \( 5(7 - 2) = 25 \) and \( 3(7) + 4 = 25 \). Both sides match.
Example 3: A quadratic equation
Solve \( x^2 - 5x + 6 = 0 \).
Look for two numbers that multiply to \( 6 \) and add to \( -5 \). Those numbers are \( -2 \) and \( -3 \), so the equation factors as:
$$ (x - 2)(x - 3) = 0 $$Set each factor equal to zero:
$$ x - 2 = 0 \quad\Rightarrow\quad x = 2 $$ $$ x - 3 = 0 \quad\Rightarrow\quad x = 3 $$Check \( x = 2 \): \( 4 - 10 + 6 = 0 \). Check \( x = 3 \): \( 9 - 15 + 6 = 0 \). Both solutions are valid.
Key formula
When a quadratic \( ax^2 + bx + c = 0 \) does not factor neatly, use the quadratic formula: \( x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Common mistake
Whatever you do to one side of an equation, do to the other side too. Subtracting a number from just one side breaks the balance and leads to a wrong answer.
How to use the equation solver
- Enter your equation. Type it in or use the equation editor for symbols like exponents, fractions, and square roots. Include the equals sign, for example \( 2x - 4 = 10 \).
- Run the solver. Press solve and our AI engine processes the equation and chooses the right method automatically.
- Read the steps. Follow the worked solution line by line, then use the final answer to check your own work or study the method.
Study tip
Try solving the equation yourself first, then compare each line with the solver. Spotting where your steps differ is one of the fastest ways to improve.
Related step-by-step guides
- How to Solve Linear Equations Step by Step — master isolating the variable and working with terms on both sides.
- How to Solve Quadratic Equations (4 Methods) — compare factoring, completing the square, the quadratic formula, and graphing.
- How to Solve for X: A Beginner’s Guide — a friendly introduction to finding the unknown in any equation.
Keep solving
Need more than equations? Explore our Algebra Solver for broader problems or the Calculus Solver for derivatives and integrals.
