need to find critical numbers of f(x) = x^4(x-1)^3

so I took the derivative using the product rule

(x-1)^3*4x^3 + x^4*3(x-1)^2

worked that out to

4x^3(x^3-3x^2+3x-1) + 3x^4(x^2-2x+1)

then I'm kinda lost its obvious one critical point is at 0 but there should be at least 1 more 2 if there is an inflection point. Please help me out I'm really lost on this stuff and these problems are due tomorrow.