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). These expressions contain one or more unknowns, which are free variables for which values are sought that cause the condition to be fulfilled. To be precise, what is sought are often not necessarily actual values, but, more in general, mathematical expressions. A solution of the equation is an assignment of expressions to the unknowns that satisfies the equation; in other words, expressions such that, when they are substituted for the unknowns, the equation becomes an identity
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What role of operations that applies when you are solving an equation does not apply when your solving an inequality?"
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An equality and equation are essentially the same thing. The equality between two expressions is represented by an equation (and conversely).
An equation is a mathematical statement that may (or may not) be true, defined for some variables. Solving an equation is finding those values of the variables for which the equation or statement is true.
Put simply, the equation for solving a cubic equation is x2 + 2ax +b = (x+a)2 + b-a2. This leads to x = -a +/- (a2 -b)1/2.