Solve xy-xz=2yz

$$xy-xz=2yz$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{2yz}{y-z}\text{, }&y\neq z\\x\in \mathrm{C}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(y-z\right)x=2yz$$

Divide both sides by y-z.

$$\frac{\left(y-z\right)x}{y-z}=\frac{2yz}{y-z}$$

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

$$x=\frac{2yz}{y-z}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{xz}{x-2z}\text{, }&x\neq 2z\\y\in \mathrm{C}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2yz from both sides.

$$xy-xz-2yz=0$$

Add xz to both sides. Anything plus zero gives itself.

$$xy-2yz=xz$$

Combine all terms containing y.

$$\left(x-2z\right)y=xz$$

Divide both sides by x-2z.

$$\frac{\left(x-2z\right)y}{x-2z}=\frac{xz}{x-2z}$$

Dividing by x-2z undoes the multiplication by x-2z.

$$y=\frac{xz}{x-2z}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2yz}{y-z}\text{, }&y\neq z\\x\in \mathrm{R}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(y-z\right)x=2yz$$

Divide both sides by y-z.

$$\frac{\left(y-z\right)x}{y-z}=\frac{2yz}{y-z}$$

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

$$x=\frac{2yz}{y-z}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{xz}{x-2z}\text{, }&x\neq 2z\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2yz from both sides.

$$xy-xz-2yz=0$$

Add xz to both sides. Anything plus zero gives itself.

$$xy-2yz=xz$$

Combine all terms containing y.

$$\left(x-2z\right)y=xz$$

Divide both sides by x-2z.

$$\frac{\left(x-2z\right)y}{x-2z}=\frac{xz}{x-2z}$$

Dividing by x-2z undoes the multiplication by x-2z.

$$y=\frac{xz}{x-2z}$$