Solve z=m-gp[m]

$$z = m - g p [ m ]$$

Solve for g

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

Steps for Solving Linear Equation

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

$$m-gpm=z$$

Subtract m from both sides.

$$-gpm=z-m$$

The equation is in standard form.

$$\left(-mp\right)g=z-m$$

Divide both sides by -pm.

$$\frac{\left(-mp\right)g}{-mp}=\frac{z-m}{-mp}$$

Dividing by -pm undoes the multiplication by -pm.

$$g=\frac{z-m}{-mp}$$

Divide z-m by -pm.

$$g=-\frac{z-m}{mp}$$

Solve for m

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

Steps for Solving Linear Equation

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

$$m-gpm=z$$

Reorder the terms.

$$-gmp+m=z$$

Combine all terms containing m.

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

The equation is in standard form.

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

Divide both sides by -gp+1.

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

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

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