[SOLVED] group theory problem 1. The problem statement, all variables and given/known data Find all solutions of the equation x^3-2x^2-3x=0 in Z_12. 2. Relevant equations 3. The attempt at a solution We first factor the polynomial into x(x-3)(x+1)=0. Recall that Z_12 is not an integral domain since 12 is not prime (e.g. 3*4=0). Therefore setting each factor equal to 0 WILL NOT GIVE ALL OF THE SOLUTIONS. Obviously, the solutions to x=0, (x-3)=0, (x+1)=0, x(x-3)=0, x(x+1) = 0, (x-3)(x+1)=0 will also be solutions to our equation. I can find all of those. The problem is that I do not know how to find the remaining ones.