Solve x^2-(a+3b)x+3ab=0

$$x ^ { 2 } - ( a + 3 b ) x + 3 a b = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=x\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=3b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+3b by x.

$$x^{2}-\left(ax+3bx\right)+3ab=0$$

To find the opposite of ax+3bx, find the opposite of each term.

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

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

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

Add 3bx to both sides.

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

Combine all terms containing a.

$$\left(-x+3b\right)a=-x^{2}+3bx$$

The equation is in standard form.

$$\left(3b-x\right)a=3bx-x^{2}$$

Divide both sides by -x+3b.

$$\frac{\left(3b-x\right)a}{3b-x}=\frac{x\left(3b-x\right)}{3b-x}$$

Dividing by -x+3b undoes the multiplication by -x+3b.

$$a=\frac{x\left(3b-x\right)}{3b-x}$$

Divide x\left(-x+3b\right) by -x+3b.

$$a=x$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=\frac{x}{3}\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=a\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+3b by x.

$$x^{2}-\left(ax+3bx\right)+3ab=0$$

To find the opposite of ax+3bx, find the opposite of each term.

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

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

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

Add ax to both sides.

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

Combine all terms containing b.

$$\left(-3x+3a\right)b=-x^{2}+ax$$

The equation is in standard form.

$$\left(3a-3x\right)b=ax-x^{2}$$

Divide both sides by -3x+3a.

$$\frac{\left(3a-3x\right)b}{3a-3x}=\frac{x\left(a-x\right)}{3a-3x}$$

Dividing by -3x+3a undoes the multiplication by -3x+3a.

$$b=\frac{x\left(a-x\right)}{3a-3x}$$

Divide x\left(-x+a\right) by -3x+3a.

$$b=\frac{x}{3}$$

Solve for a

$$\left\{\begin{matrix}\\a=x\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=3b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+3b by x.

$$x^{2}-\left(ax+3bx\right)+3ab=0$$

To find the opposite of ax+3bx, find the opposite of each term.

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

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

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

Add 3bx to both sides.

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

Combine all terms containing a.

$$\left(-x+3b\right)a=-x^{2}+3bx$$

The equation is in standard form.

$$\left(3b-x\right)a=3bx-x^{2}$$

Divide both sides by -x+3b.

$$\frac{\left(3b-x\right)a}{3b-x}=\frac{x\left(3b-x\right)}{3b-x}$$

Dividing by -x+3b undoes the multiplication by -x+3b.

$$a=\frac{x\left(3b-x\right)}{3b-x}$$

Divide x\left(-x+3b\right) by -x+3b.

$$a=x$$

Solve for b

$$\left\{\begin{matrix}\\b=\frac{x}{3}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=a\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+3b by x.

$$x^{2}-\left(ax+3bx\right)+3ab=0$$

To find the opposite of ax+3bx, find the opposite of each term.

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

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

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

Add ax to both sides.

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

Combine all terms containing b.

$$\left(-3x+3a\right)b=-x^{2}+ax$$

The equation is in standard form.

$$\left(3a-3x\right)b=ax-x^{2}$$

Divide both sides by -3x+3a.

$$\frac{\left(3a-3x\right)b}{3a-3x}=\frac{x\left(a-x\right)}{3a-3x}$$

Dividing by -3x+3a undoes the multiplication by -3x+3a.

$$b=\frac{x\left(a-x\right)}{3a-3x}$$

Divide x\left(-x+a\right) by -3x+3a.

$$b=\frac{x}{3}$$