How can I isolate y? y>0

55(1-y^20) = (1 - y^10)[30 + 60y^10 + 90y^20]

I'm having a really tough time. I get to:

0 = -3y^30 + 2.83 y^20 + y^10 - 0.83

I have no idea how to solve this kind of equation. Help?

(I realize I could replace y^10 = x, say, and get a third degree polynomial, but I'm not in the measure of solving such an equation ...)