Solve ax^2-ax=x-3

$$a x ^ { 2 } - a x = x - 3$$

Solve for a

$$a=-\frac{3-x}{x\left(x-1\right)}$$

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Combine all terms containing a.

$$\left(x^{2}-x\right)a=x-3$$

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

$$\frac{\left(x^{2}-x\right)a}{x^{2}-x}=\frac{x-3}{x^{2}-x}$$

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

$$a=\frac{x-3}{x^{2}-x}$$

Divide x-3 by x^{2}-x.

$$a=\frac{x-3}{x\left(x-1\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{a^{2}-10a+1}+a+1}{2a}\text{; }x=\frac{-\sqrt{a^{2}-10a+1}+a+1}{2a}\text{, }&a\neq 0\\x=3\text{, }&a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{a^{2}-10a+1}+a+1}{2a}\text{; }x=\frac{-\sqrt{a^{2}-10a+1}+a+1}{2a}\text{, }&\left(a\neq 0\text{ and }a\leq 5-2\sqrt{6}\right)\text{ or }a\geq 2\sqrt{6}+5\\x=3\text{, }&a=0\end{matrix}\right.$$