Solve x^2-mx+mx-mn=0

$$x ^ { 2 } - m x + m x - m n = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{x^{2}}{n}\text{, }&n\neq 0\\m\in \mathrm{C}\text{, }&x=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine -mx and mx to get 0.

$$x^{2}-mn=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-mn=-x^{2}$$

Cancel out -1 on both sides.

$$mn=x^{2}$$

The equation is in standard form.

$$nm=x^{2}$$

Divide both sides by n.

$$\frac{nm}{n}=\frac{x^{2}}{n}$$

Dividing by n undoes the multiplication by n.

$$m=\frac{x^{2}}{n}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{x^{2}}{m}\text{, }&m\neq 0\\n\in \mathrm{C}\text{, }&x=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine -mx and mx to get 0.

$$x^{2}-mn=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-mn=-x^{2}$$

Cancel out -1 on both sides.

$$mn=x^{2}$$

Divide both sides by m.

$$\frac{mn}{m}=\frac{x^{2}}{m}$$

Dividing by m undoes the multiplication by m.

$$n=\frac{x^{2}}{m}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{x^{2}}{n}\text{, }&n\neq 0\\m\in \mathrm{R}\text{, }&x=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine -mx and mx to get 0.

$$x^{2}-mn=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-mn=-x^{2}$$

Cancel out -1 on both sides.

$$mn=x^{2}$$

The equation is in standard form.

$$nm=x^{2}$$

Divide both sides by n.

$$\frac{nm}{n}=\frac{x^{2}}{n}$$

Dividing by n undoes the multiplication by n.

$$m=\frac{x^{2}}{n}$$

Solve for n

$$\left\{\begin{matrix}n=\frac{x^{2}}{m}\text{, }&m\neq 0\\n\in \mathrm{R}\text{, }&x=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine -mx and mx to get 0.

$$x^{2}-mn=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-mn=-x^{2}$$

Cancel out -1 on both sides.

$$mn=x^{2}$$

Divide both sides by m.

$$\frac{mn}{m}=\frac{x^{2}}{m}$$

Dividing by m undoes the multiplication by m.

$$n=\frac{x^{2}}{m}$$