Solution of $x^3+x^2-12x=0$ in $\mathbb{Z}_{11}$ I am trying to solve $x^3+x^2-12x=0$ in $\mathbb Z_{11}$. I find $3$ solutions: $0, 3$ and $7$ but the book claims that there are only $2$ solutions. Am i doing something wrong?
Thank you

What you have is right.$$x^3+x^2-12x = x(x+4)(x-3) \equiv 0 \pmod{11}$$
Hence,
$$x \equiv 0,3,7 \pmod{11}$$
