$$32k-32=-5k-32$$Add $5k$ to both sides.
$$32k-32+5k=-32$$Combine $32k$ and $5k$ to get $37k$.
$$37k-32=-32$$Add $32$ to both sides.
$$37k=-32+32$$Add $-32$ and $32$ to get $0$.
$$37k=0$$Product of two numbers is equal to $0$ if at least one of them is $0$. Since $37$ is not equal to $0$, $k$ must be equal to $0$.