Math Equation Solver

Math equation solver at a glance#

A math equation solver simplifies an expression or finds the value of a variable. For a plain expression it follows the order of operations, PEMDAS: parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right. For an equation it isolates the variable so both sides stay equal.

How does order of operations work?#

Work through PEMDAS one step at a time. In 12 + 7 * 2 you do the multiplication first, 7 * 2 = 14, then the addition, 12 + 14 = 26. In (2^3) * (3 + 5) you handle the exponent and the parentheses first, 2^3 = 8 and 3 + 5 = 8, then multiply, 8 * 8 = 64. Changing that order changes the answer, which is why the rule exists.

How do you solve an equation for a variable?#

Do the same operation to both sides until the variable stands alone. To solve 2x + 5 = 15, subtract 5 from both sides to get 2x = 10, then divide both sides by 2 to get x = 5. You can check it by putting 5 back in: 2 times 5 plus 5 is 15, which matches. The same balancing idea extends to quadratic equations, where the solver applies the quadratic formula instead.

Enter your expression or equation in the calculator above for the worked result with each step shown. Use ^ for exponents and r for roots, for example 16r2 for the square root of 16, and keep your parentheses balanced so the order of operations reads the way you intend.

What this solver handles#

This tool does two jobs. It simplifies a numeric expression using the order of operations, and it solves a basic algebra equation for one variable, including linear and quadratic equations. It is not a full computer-algebra system, so very advanced calculus or symbolic work is out of scope. Type your expression or equation into the calculator above and it shows the worked steps.

PEMDAS, the order of operations#

For a plain expression, the solver follows PEMDAS so every part is handled in the right order: parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right. The order matters. In 20 - 6 / 2 you divide first, 6 / 2 = 3, then subtract, 20 - 3 = 17; doing it left to right instead would give the wrong answer. In 4 + 3 × 5 the multiplication comes first, 3 × 5 = 15, then 4 + 15 = 19.

Symbols you can type#

Use the standard keyboard symbols: + for addition, - for subtraction, * for multiplication, / for division, ^ for exponents (3^4 means 3 to the fourth power), and r for roots (16r2 is the square root of 16). Keep parentheses balanced, because the solver reads them first and unmatched brackets change the order of operations.

Solving for a variable#

To solve a linear equation, do the same operation to both sides until the variable stands alone. For 2x + 5 = 15, subtract 5 from both sides to get 2x = 10, then divide by 2 to get x = 5; check it by putting 5 back in, since 2 × 5 + 5 = 15. Quadratic equations, the kind with an x² term, are solved with the quadratic formula, which can return two answers.

Math equation solver FAQ#

What is a math equation solver?#

It simplifies a numeric expression by the PEMDAS order of operations and solves a basic algebra equation for one variable. It shows each step, so you can follow how the answer was reached.

Can it solve linear equations?#

Yes. It isolates the variable step by step, the same operation on both sides. For 2x + 5 = 15 it returns x = 5.

Can it solve quadratic equations?#

Yes. For an equation with an x² term it applies the quadratic formula and reports the roots, which may be two values, one repeated value, or none in the real numbers.

How does it apply the order of operations?#

It works through PEMDAS one stage at a time: parentheses, exponents, then multiplication and division left to right, then addition and subtraction left to right. So 20 - 6 / 2 = 17, not 7.

How do I enter an equation?#

Type it with standard symbols (+, -, *, /, ^ for exponents, r for roots), keep parentheses balanced, then press solve. The result lists each step in order.