TITLE: Algebra solve for x
QUESTION [7 upvotes]: I tried to solve for x in the equation $x^3=x$. I did 
$$x^3=x$$
$$x^2=1$$
$$x=\pm1$$
but it's wrong, can anyone help.

REPLY [10 votes]: 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 $$x=-1,0,1$$