Literal equation solver

Enter a formula such as y = m*x + b and choose x to receive x = (y - b) / m, along with normalized input, remaining symbols, and concise steps. The solver handles equations that are linear in the target, including parentheses, explicit or implied multiplication, and division by expressions that do not contain that target. It runs deterministically in the browser, while the same result is available through the API for $0.002 per successful request.

What it means to solve a literal equation for one variable

A literal equation is a relationship among named quantities rather than an equation containing only one unknown and several fixed numbers. Familiar examples include distance equals rate times time, force equals mass times acceleration, and a straight-line equation written as y equals m times x plus b. To solve one of these formulas for a selected variable, every operation applied to that variable must be undone while equality is preserved. If y equals m times x plus b, subtracting b from both sides gives y minus b equals m times x, and dividing both sides by m gives x equals the quantity y minus b divided by m. This solver performs that rearrangement symbolically. Its response contains the target, the isolated expression, a complete solved equation, a normalized version of the original input, the other variables that remain, and a short sequence of algebra instructions. Symbols are not assigned hidden values, so the result remains a reusable formula. The tool focuses on equations that are linear in the chosen target: the target may occur in sums, differences, multiplication by target-free factors, and numerators divided by target-free expressions. That scope covers many classroom, science, engineering, finance, and spreadsheet formulas while keeping the answer transparent and deterministic. A result should still be read with the original formula's domain restrictions in mind, especially when the final step divides by a symbolic coefficient that must be nonzero.

How to enter formulas and understand supported rearrangements

Provide exactly one equals sign and name the variable you want isolated. Identifiers begin with a letter or underscore and may continue with letters, digits, or underscores, so names such as velocity, r2, and initial_speed are valid. The parser accepts decimal numbers, parentheses, addition, subtraction, multiplication, division, and exponentiation. You may write multiplication explicitly as m*x or imply it with adjacency as mx only when the intended symbols are unambiguous: because mx is read as one identifier, write m x, m*x, or m(x) when m and x are separate variables. Parentheses can group a factor or numerator, and ordinary operator precedence is respected. The solver examines both sides and represents each as a symbolic coefficient times the target plus a target-free remainder. It then subtracts the coefficients, moves the remainders, and divides once to isolate the requested identifier. A formula may contain powers of other symbols, but the chosen target must occur only to the first power. The solver deliberately rejects target variables in denominators, powers, or both factors of the same product, because those structures are nonlinear and may require multiple branches or extra assumptions. It also rejects equations in which the target disappears after like terms are collected, since such an equation is either an identity or a contradiction rather than a unique symbolic solution. Error messages identify these limits instead of presenting a plausible-looking but incomplete rearrangement. Inputs are capped at 1,000 characters and 300 tokens to keep browser and API execution bounded.

Using isolated formulas accurately in study and technical work

Rearranged formulas are useful wherever the known and unknown quantities change from one calculation to the next. A physics student can turn F = m*a into a = F / m before substituting measurements. An electronics worksheet can isolate current, resistance, or voltage from a linear form, while a geometry exercise can rearrange a perimeter relationship for one dimension. In software, the symbolic expression can become a documented implementation rule, a test fixture, or a check against a formula copied from a specification. Analysts can rearrange affine pricing and forecasting equations before placing them into a spreadsheet cell. Teachers can use the returned steps to emphasize that the same operation is applied to both sides rather than treating transposition as an unexplained sign-changing trick. Always retain mathematical conditions implied by division: solving m*x = y for x produces y / m, which assumes m is not zero. Also verify units after rearrangement; dimensional consistency is a powerful way to catch an incorrectly entered formula even when its algebra is syntactically valid. This capability does not substitute numerical values, simplify with domain-specific identities, choose among roots, or solve trigonometric, logarithmic, or general polynomial equations. Those problems need solvers that can describe branches and domains. For supported linear literal equations, however, execution is pure and reproducible: identical text and target produce identical JSON without a network request, random choice, stored state, or time-dependent value. Interactive browser use is free, and a successful API call costs $0.002 when you need the same rearrangement in an automated workflow.