I'm not sure what you mean by "simplify". That's about as simple as it is going to get. And, as for actually finding the roots, I doubt you will be able to do that. There is a "quartic equation" but it is very complicated.
You can, for example, use the "rational root theorem" that says that if is a root of a polynomial with integer coefficients then n must divide the leading coefficient and m must divide the constant term. Here the leading coefficient is 1 and the constant term is 3 which has only and as its divisors. It is easy to see that , , , and , none of which are 0 so all roots are irrational numbers.
You can, for example, determine that while, as above, the value at 1 is -1< 0. That means there must be a root between 0 and 1. so there is another root between 1 and 2. I believe, though I can't prove it, that the other two roots are not real numbers.