In
mathematics, to
solve an equation is to find what values (
numbers,
functions,
sets, etc.) fulfill a condition stated in the form of an
equation (two
expressions related by
equality). When searching a solution, one or more
free variables are designated as
unknowns. A solution is an assignment of expressions to the unknown variables that makes the equality in the equation true. In other words, a solution is an expression or a collection of expressions (one for each unknown) such that, when
substituted for the unknowns, the equation becomes an
identity. A problem of solving an equation may be numeric or symbolic. Solving an equation
numerically means that only numbers represented literately (not as a combination of variables), are admitted as solutions. Solving an equation
symbolically means that expressions that may contain known variables or possibly also variables not in the original equation are admitted as solutions.