Solve y=ax^2-2ax

$$y = a x ^ { 2 } - 2 a x$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

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

Combine all terms containing a.

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

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

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

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

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

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

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

Solve for a

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

Steps for Solving Linear Equation

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

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

Combine all terms containing a.

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

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

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

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

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

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

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

Solve for x (complex solution)

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

Solve for x

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