You can approximate the solution by doing what excel calls Goal Seek - testing values for x until both sides of the equation approximately match. You can do this by splitting the equation by the = sign, replacing each occurence of x with a value, evaling both sides, and determining if the difference falls below a certain threshold. While relatively simple, there are flaws to this method though (other than the fact that it is an approximation), for example the algorithm may think the two sides are converging when in fact it is just a local min/max and will diverge after the difference falls just below your threshold. You'll also need to test multiple start points to solve equations with more than one solution.

For a program to actually solve an equation as a human would (by rearranging the two sides of the equation and applying inverse functions, derivatives/integrals and whatnot) is far more complex, and somehow feels entirely proprietary ;)