Solve ax+bx-ab=x^2

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ax-ab=x^{2}-bx$$

Combine all terms containing a.

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

Divide both sides by x-b.

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

Dividing by x-b undoes the multiplication by x-b.

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

Divide x\left(x-b\right) by x-b.

$$a=x$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$bx-ab=x^{2}-ax$$

Combine all terms containing b.

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

Divide both sides by x-a.

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

Dividing by x-a undoes the multiplication by x-a.

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

Divide x\left(x-a\right) by x-a.

$$b=x$$

Solve for a

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

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ax-ab=x^{2}-bx$$

Combine all terms containing a.

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

Divide both sides by x-b.

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

Dividing by x-b undoes the multiplication by x-b.

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

Divide x\left(x-b\right) by x-b.

$$a=x$$

Solve for b

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$bx-ab=x^{2}-ax$$

Combine all terms containing b.

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

Divide both sides by x-a.

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

Dividing by x-a undoes the multiplication by x-a.

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

Divide x\left(x-a\right) by x-a.

$$b=x$$