Question

How do you solve algebra equations with a variable to several powers?

Answer 1

If you have one variable and a power not greater then 4 there are solution formulas.
http://en.wikipedia.org/wiki/Quartic_function
For higher orders there is no analytic solution anymore. But of course you can guess a root x_0 and factorize (x - x_0) from polynomial, getting a polynomial of one degree less. If the polynomial has only integer roots, they divide the constant part.