Solve kx=my-mx

$$k x = m y - m x$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{m\left(y-x\right)}{x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&\left(m=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xk=my-mx$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{m\left(y-x\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{m\left(y-x\right)}{x}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{kx}{x-y}\text{, }&x\neq y\\m\in \mathrm{C}\text{, }&\left(k=0\text{ and }x=y\right)\text{ or }\left(x=0\text{ and }y=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$my-mx=kx$$

Combine all terms containing m.

$$\left(y-x\right)m=kx$$

Divide both sides by y-x.

$$\frac{\left(y-x\right)m}{y-x}=\frac{kx}{y-x}$$

Dividing by y-x undoes the multiplication by y-x.

$$m=\frac{kx}{y-x}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{m\left(y-x\right)}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&\left(m=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xk=my-mx$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{m\left(y-x\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{m\left(y-x\right)}{x}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{kx}{x-y}\text{, }&x\neq y\\m\in \mathrm{R}\text{, }&\left(k=0\text{ and }x=y\right)\text{ or }\left(x=0\text{ and }y=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$my-mx=kx$$

Combine all terms containing m.

$$\left(y-x\right)m=kx$$

Divide both sides by y-x.

$$\frac{\left(y-x\right)m}{y-x}=\frac{kx}{y-x}$$

Dividing by y-x undoes the multiplication by y-x.

$$m=\frac{kx}{y-x}$$