Solve ax-a=a^2

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

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=a+1\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add a to both sides.

$$ax=a^{2}+a$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{a\left(a+1\right)}{a}$$

Dividing by a undoes the multiplication by a.

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

Divide a\left(1+a\right) by a.

$$x=a+1$$

Solve for x

$$\left\{\begin{matrix}\\x=a+1\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add a to both sides.

$$ax=a^{2}+a$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{a\left(a+1\right)}{a}$$

Dividing by a undoes the multiplication by a.

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

Divide a\left(1+a\right) by a.

$$x=a+1$$

Solve for a

$$a=x-1$$

$$a=0$$