Solve y=mx^2-2mx+2

$$y = m x ^ { 2 } - 2 m x + 2$$

Solve for m (complex solution)

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

Steps for Solving Linear Equation

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

$$mx^{2}-2mx+2=y$$

Subtract 2 from both sides.

$$mx^{2}-2mx=y-2$$

Combine all terms containing m.

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

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

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

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

$$m=\frac{y-2}{x^{2}-2x}$$

Divide y-2 by x^{2}-2x.

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

Solve for m

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

Steps for Solving Linear Equation

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

$$mx^{2}-2mx+2=y$$

Subtract 2 from both sides.

$$mx^{2}-2mx=y-2$$

Combine all terms containing m.

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

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

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

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

$$m=\frac{y-2}{x^{2}-2x}$$

Divide y-2 by x^{2}-2x.

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

Solve for x (complex solution)

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

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{m\left(y+m-2\right)}+m}{m}\text{; }x=\frac{-\sqrt{m\left(y+m-2\right)}+m}{m}\text{, }&m\neq 0\text{ and }\left(m>0\text{ or }y\leq 2-m\right)\text{ and }\left(m<0\text{ or }y\geq 2-m\right)\\x\in \mathrm{R}\text{, }&m=0\text{ and }y=2\end{matrix}\right.$$