Find all solutions to x^3-2x^2-3x=0 in Z12

Solutions can be found by factoring:

x^3-2x^2-3x

=x (x^2-2*x-3)

=x (x+1) (x-3)

By the zero product theorem,

x=0, or

(x+1) = 0 = > x=-1, or

(x-3) = 0 = > x=3

Therefore the solutions are

{-1,0,3}