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

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x\left(nx-3b\right)}{3b-x}\text{, }&x\neq 3b\\a\in \mathrm{C}\text{, }&\left(n=1\text{ and }b\neq 0\text{ and }x=3b\right)\text{ or }\left(b=0\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add 3bx to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -x+3b.

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

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

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

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{x\left(nx-a\right)}{3\left(a-x\right)}\text{, }&x\neq a\\b\in \mathrm{C}\text{, }&\left(n=1\text{ and }a\neq 0\text{ and }x=a\right)\text{ or }\left(a=0\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add ax to both sides.

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

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -3x+3a.

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

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

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

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

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{x\left(nx-3b\right)}{3b-x}\text{, }&x\neq 3b\\a\in \mathrm{R}\text{, }&\left(n=1\text{ and }b\neq 0\text{ and }x=3b\right)\text{ or }\left(b=0\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add 3bx to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -x+3b.

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

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

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

Solve for b

$$\left\{\begin{matrix}b=-\frac{x\left(nx-a\right)}{3\left(a-x\right)}\text{, }&x\neq a\\b\in \mathrm{R}\text{, }&\left(n=1\text{ and }a\neq 0\text{ and }x=a\right)\text{ or }\left(a=0\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add ax to both sides.

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

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -3x+3a.

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

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

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

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

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