Solve x^2-ax-bx+ab=0

$$x ^ { 2 } - a x - b x + a b = 0$$

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 x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add bx to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -x+b.

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

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

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

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

$$a=x$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add ax to both sides.

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

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -x+a.

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

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

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

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 x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add bx to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -x+b.

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

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

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

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

$$a=x$$

Solve for b

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add ax to both sides.

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

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -x+a.

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

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

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

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

$$b=x$$