Solve MK+MZ=K

$$M K + M Z = K$$

Solve for K (complex solution)

$$\left\{\begin{matrix}K=-\frac{MZ}{M-1}\text{, }&M\neq 1\\K\in \mathrm{C}\text{, }&Z=0\text{ and }M=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract K from both sides.

$$MK+MZ-K=0$$

Subtract MZ from both sides. Anything subtracted from zero gives its negation.

$$MK-K=-MZ$$

Reorder the terms.

$$KM-K=-MZ$$

Combine all terms containing K.

$$\left(M-1\right)K=-MZ$$

Divide both sides by M-1.

$$\frac{\left(M-1\right)K}{M-1}=-\frac{MZ}{M-1}$$

Dividing by M-1 undoes the multiplication by M-1.

$$K=-\frac{MZ}{M-1}$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=\frac{K}{K+Z}\text{, }&K\neq -Z\\M\in \mathrm{C}\text{, }&K=0\text{ and }Z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing M.

$$\left(K+Z\right)M=K$$

Divide both sides by K+Z.

$$\frac{\left(K+Z\right)M}{K+Z}=\frac{K}{K+Z}$$

Dividing by K+Z undoes the multiplication by K+Z.

$$M=\frac{K}{K+Z}$$

Solve for K

$$\left\{\begin{matrix}K=-\frac{MZ}{M-1}\text{, }&M\neq 1\\K\in \mathrm{R}\text{, }&Z=0\text{ and }M=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract K from both sides.

$$MK+MZ-K=0$$

Subtract MZ from both sides. Anything subtracted from zero gives its negation.

$$MK-K=-MZ$$

Reorder the terms.

$$KM-K=-MZ$$

Combine all terms containing K.

$$\left(M-1\right)K=-MZ$$

Divide both sides by M-1.

$$\frac{\left(M-1\right)K}{M-1}=-\frac{MZ}{M-1}$$

Dividing by M-1 undoes the multiplication by M-1.

$$K=-\frac{MZ}{M-1}$$

Solve for M

$$\left\{\begin{matrix}M=\frac{K}{K+Z}\text{, }&K\neq -Z\\M\in \mathrm{R}\text{, }&K=0\text{ and }Z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing M.

$$\left(K+Z\right)M=K$$

Divide both sides by K+Z.

$$\frac{\left(K+Z\right)M}{K+Z}=\frac{K}{K+Z}$$

Dividing by K+Z undoes the multiplication by K+Z.

$$M=\frac{K}{K+Z}$$