Solve (x-a)(x+b)=3bx

$$( x - a ) ( x + b ) = 3 b x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{x\left(x-2b\right)}{x+b}\text{, }&x\neq -b\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+xb-ax-ab=3bx$$

Subtract x^{2} from both sides.

$$xb-ax-ab=3bx-x^{2}$$

Subtract xb from both sides.

$$-ax-ab=3bx-x^{2}-xb$$

Combine 3bx and -xb to get 2bx.

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

Combine all terms containing a.

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

Divide both sides by -x-b.

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

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

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

Divide x\left(2b-x\right) by -x-b.

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

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{x\left(x-a\right)}{2x+a}\text{, }&x\neq -\frac{a}{2}\\b\in \mathrm{C}\text{, }&x=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+xb-ax-ab=3bx$$

Subtract 3bx from both sides.

$$x^{2}+xb-ax-ab-3bx=0$$

Combine xb and -3bx to get -2xb.

$$x^{2}-2xb-ax-ab=0$$

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

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

Add ax to both sides.

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

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -2x-a.

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

Dividing by -2x-a undoes the multiplication by -2x-a.

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

Divide x\left(-x+a\right) by -2x-a.

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

Solve for a

$$\left\{\begin{matrix}a=\frac{x\left(x-2b\right)}{x+b}\text{, }&x\neq -b\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+xb-ax-ab=3bx$$

Subtract x^{2} from both sides.

$$xb-ax-ab=3bx-x^{2}$$

Subtract xb from both sides.

$$-ax-ab=3bx-x^{2}-xb$$

Combine 3bx and -xb to get 2bx.

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

Combine all terms containing a.

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

Divide both sides by -x-b.

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

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

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

Divide x\left(2b-x\right) by -x-b.

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

Solve for b

$$\left\{\begin{matrix}b=\frac{x\left(x-a\right)}{2x+a}\text{, }&x\neq -\frac{a}{2}\\b\in \mathrm{R}\text{, }&x=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+xb-ax-ab=3bx$$

Subtract 3bx from both sides.

$$x^{2}+xb-ax-ab-3bx=0$$

Combine xb and -3bx to get -2xb.

$$x^{2}-2xb-ax-ab=0$$

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

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

Add ax to both sides.

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

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -2x-a.

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

Dividing by -2x-a undoes the multiplication by -2x-a.

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

Divide x\left(-x+a\right) by -2x-a.

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