Algebra solve for x

You forgot 0. You shouldn't divide by x, or else you will miss it. You can solve it like this:

$$x^3=x$$ subtract x from both sides$$x^3-x=0$$ factor out x$$x(x^2-1)=0$$factor $x^2-1$ $$x(x+1)(x-1)=0$$ Simplify $$x=-1,0,1$$