Proving $x-8$ is equal to $x^{2}- 64$

Question

Okay so I have this trick question that I can't seem to figure out. Suppose $x = 8$ and $x^2 = 64$, then $x -8 = 0$ and
$ x^2- 64 = 0 $. Now comparing both since they are equal to zero, $x - 8 = x^2 - 64 \Rightarrow x - 8 = (x+8) (x-8) \Rightarrow 1 = (x + 8)$, Substituting value of $x$ gives, $1 = 16$ which is not true. I'd appreciate if someone can help me figure out the mistake here.

Answer 1

You divided both sides of the equation by $0 = x-8,$ which you cannot do.