# Solve for $x$, when $x^2-2x=0$

Probably a dumb question, but solving this:

$$x^2=2x$$ $$x=2$$

But also (or using the quadratic formula);

$$x^2-2x=0$$

$$x(x-2)=0$$ $$x=0/x=2$$

Is the first computation wrong, and why is it limiting?

• In the first part of the question, you are dividing by $x$ to simplify. This is valid if $x \ne 0$, and $x = 0$ is a solution. – user296602 Nov 2 '17 at 17:05

In the first part, you can «cancel» the $x$ therm if $x\not = 0$. If you cancel that term, you are asuming implicitly that $x\neq 0$.