Solve equation for x: $m^2(z^2-25)=n^2(z^2-25)$

Question

$$m^2(z^2-25)=n^2(z^2-25)$$

I don't get it? I don't even have x anywhere in this equation. Can somebody make this a bit clearer?

Answer 1

It's $$(m^2-n^2)(z^2-25)=0.$$

If $m^2=n^2$ we get $\mathbb R$.

If $m^2\neq n^2$ we get $z^2=25$, which gives $\{-5,5\}$.