That's not a polynomial, it doesn't have positive integer exponents (because )
Otherwise I have no idea how to solve this, I just wanted to point that out.
In general, there is no easy way to solve polynomials. The polynomial here is a quartic, which can be solved (although not easily) following the approach found here:
Quartic function - Wikipedia, the free encyclopedia
A similar approach can solve quintics (polynomials of degree 5) but there is no general method for solving higher order polynomials
Linear and quadratics are easy because mathematicians have found a highly efficient and easy way to solve them. Cubic polynomials are quite harder (but still solvable in most situations), quartics get hard and quintics even harder (wanna try elliptic curves ?). And for higher degree ... well badgerigar sait it all