Ok, I'm assuming you're solving for the zero's? Which is basically the x-intercepts (Places where the graph crosses the x axis.
First, I graphed the line 3x^4+5x^3-10x^2-20x-8
and it crosses over the x axis at 4 spots: x=-1,-2,-2/3,2
so that means when we factor out the quadratic, we should have something like:
(3x+2)(x+1)(x-2)(x+2)
so when you foil all that out, you should get the original equation.
I used desmos graphing calculator (google it) and wolframalpha to help factor.
Good luck!