Solve x^2-x(a-b)-ab=0

$$x ^ { 2 } - x ( a - b ) - a b = 0$$

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

Use the distributive property to multiply x by a-b.

$$x^{2}-\left(xa-xb\right)-ab=0$$

To find the opposite of xa-xb, find the opposite of each term.

$$x^{2}-xa+xb-ab=0$$

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

$$-xa+xb-ab=-x^{2}$$

Subtract xb from both sides.

$$-xa-ab=-x^{2}-xb$$

Combine all terms containing a.

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

The equation is in standard form.

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

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)

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

Steps for Solving Linear Equation

Use the distributive property to multiply x by a-b.

$$x^{2}-\left(xa-xb\right)-ab=0$$

To find the opposite of xa-xb, find the opposite of each term.

$$x^{2}-xa+xb-ab=0$$

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

$$-xa+xb-ab=-x^{2}$$

Add xa to both sides.

$$xb-ab=-x^{2}+xa$$

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by x-a.

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

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

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

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

Use the distributive property to multiply x by a-b.

$$x^{2}-\left(xa-xb\right)-ab=0$$

To find the opposite of xa-xb, find the opposite of each term.

$$x^{2}-xa+xb-ab=0$$

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

$$-xa+xb-ab=-x^{2}$$

Subtract xb from both sides.

$$-xa-ab=-x^{2}-xb$$

Combine all terms containing a.

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

The equation is in standard form.

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

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

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

Steps for Solving Linear Equation

Use the distributive property to multiply x by a-b.

$$x^{2}-\left(xa-xb\right)-ab=0$$

To find the opposite of xa-xb, find the opposite of each term.

$$x^{2}-xa+xb-ab=0$$

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

$$-xa+xb-ab=-x^{2}$$

Add xa to both sides.

$$xb-ab=-x^{2}+xa$$

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by x-a.

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

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

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

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

$$b=-x$$