How do you solve a cubic equation?

If you can find a simple factoring of the cubic polynomial, then it is fairly easy to solve (by the zero-product property). Otherwise it isn't; there are several iterative methods, but none of them is simple. That's why the solution of polynomials of degree is usually not covered in high school, or even in college.

If you are really interested in the more or less complicated details, the Wikipedia article on "Root-finding algorithm" gives you an introduction.