Solve nx(x-4)+2n=m

$$n x ( x - 4 ) + 2 n = m$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{m}{x^{2}-4x+2}\text{, }&x\neq \sqrt{2}+2\text{ and }x\neq 2-\sqrt{2}\\n\in \mathrm{C}\text{, }&\left(x=2-\sqrt{2}\text{ or }x=\sqrt{2}+2\right)\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply nx by x-4.

$$nx^{2}-4nx+2n=m$$

Combine all terms containing n.

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

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

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

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

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

Solve for n

$$\left\{\begin{matrix}n=\frac{m}{x^{2}-4x+2}\text{, }&x\neq \sqrt{2}+2\text{ and }x\neq 2-\sqrt{2}\\n\in \mathrm{R}\text{, }&\left(x=2-\sqrt{2}\text{ or }x=\sqrt{2}+2\right)\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply nx by x-4.

$$nx^{2}-4nx+2n=m$$

Combine all terms containing n.

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

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

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

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

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

Solve for m

$$m=n\left(x\left(x-4\right)+2\right)$$