Solve mx^2-4mx+n=0

$$m x ^ { 2 } - 4 m x + n = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{n}{x\left(x-4\right)}\text{, }&x\neq 4\text{ and }x\neq 0\\m\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=4\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mx^{2}-4mx=-n$$

Combine all terms containing m.

$$\left(x^{2}-4x\right)m=-n$$

Divide both sides by x^{2}-4x.

$$\frac{\left(x^{2}-4x\right)m}{x^{2}-4x}=-\frac{n}{x^{2}-4x}$$

Dividing by x^{2}-4x undoes the multiplication by x^{2}-4x.

$$m=-\frac{n}{x^{2}-4x}$$

Divide -n by x^{2}-4x.

$$m=-\frac{n}{x\left(x-4\right)}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{n}{x\left(x-4\right)}\text{, }&x\neq 4\text{ and }x\neq 0\\m\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=4\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mx^{2}-4mx=-n$$

Combine all terms containing m.

$$\left(x^{2}-4x\right)m=-n$$

Divide both sides by x^{2}-4x.

$$\frac{\left(x^{2}-4x\right)m}{x^{2}-4x}=-\frac{n}{x^{2}-4x}$$

Dividing by x^{2}-4x undoes the multiplication by x^{2}-4x.

$$m=-\frac{n}{x^{2}-4x}$$

Divide -n by x^{2}-4x.

$$m=-\frac{n}{x\left(x-4\right)}$$

Solve for n

$$n=-mx\left(x-4\right)$$