Solve z=m-9pm

$$z = m-9pm$$

Solve for m

$$\left\{\begin{matrix}m=\frac{z}{1-9p}\text{, }&p\neq \frac{1}{9}\\m\in \mathrm{R}\text{, }&z=0\text{ and }p=\frac{1}{9}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$m-9pm=z$$

Combine all terms containing m.

$$\left(1-9p\right)m=z$$

Divide both sides by 1-9p.

$$\frac{\left(1-9p\right)m}{1-9p}=\frac{z}{1-9p}$$

Dividing by 1-9p undoes the multiplication by 1-9p.

$$m=\frac{z}{1-9p}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{z}{9m}+\frac{1}{9}\text{, }&m\neq 0\\p\in \mathrm{R}\text{, }&z=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$m-9pm=z$$

Subtract m from both sides.

$$-9pm=z-m$$

The equation is in standard form.

$$\left(-9m\right)p=z-m$$

Divide both sides by -9m.

$$\frac{\left(-9m\right)p}{-9m}=\frac{z-m}{-9m}$$

Dividing by -9m undoes the multiplication by -9m.

$$p=\frac{z-m}{-9m}$$

Divide z-m by -9m.

$$p=-\frac{z}{9m}+\frac{1}{9}$$