On problems like $\displaystyle -12x^3+12x^2+24x $

I try to solve for roots.

What I get is, (12+x)(-x^2+x+2), leaving me to find

x=-12 x=-1 x=2

Come to find out, x=-12 should be x=0. How can I fix this?

Also, for problems that do not factor so easy, $\displaystyle -32x^3+12x+0 $, what are some factor methods? thank you