Solve z=m-qp(m)

$$z = m - q p ( m )$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{z}{pq-1}\text{, }&p=0\text{ or }q\neq \frac{1}{p}\\m\in \mathrm{R}\text{, }&z=0\text{ and }q=\frac{1}{p}\text{ and }p\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$m-qpm=z$$

Reorder the terms.

$$-mpq+m=z$$

Combine all terms containing m.

$$\left(-pq+1\right)m=z$$

The equation is in standard form.

$$\left(1-pq\right)m=z$$

Divide both sides by -pq+1.

$$\frac{\left(1-pq\right)m}{1-pq}=\frac{z}{1-pq}$$

Dividing by -pq+1 undoes the multiplication by -pq+1.

$$m=\frac{z}{1-pq}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{m-z}{mq}\text{, }&m\neq 0\text{ and }q\neq 0\\p\in \mathrm{R}\text{, }&\left(z=m\text{ and }q=0\right)\text{ or }\left(z=0\text{ and }m=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$m-qpm=z$$

Subtract m from both sides.

$$-qpm=z-m$$

The equation is in standard form.

$$\left(-mq\right)p=z-m$$

Divide both sides by -qm.

$$\frac{\left(-mq\right)p}{-mq}=\frac{z-m}{-mq}$$

Dividing by -qm undoes the multiplication by -qm.

$$p=\frac{z-m}{-mq}$$

Divide z-m by -qm.

$$p=-\frac{z-m}{mq}$$