Variable $z$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $10z$, the least common multiple of $z,10$.
$$10\left(-30\right)=z\times 40$$
Multiply $10$ and $-30$ to get $-300$.
$$-300=z\times 40$$
Swap sides so that all variable terms are on the left hand side.
$$z\times 40=-300$$
Divide both sides by $40$.
$$z=\frac{-300}{40}$$
Reduce the fraction $\frac{-300}{40}$ to lowest terms by extracting and canceling out $20$.
