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

$$- ( a + 3 b ) x + 3 a b = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{3bx}{3b-x}\text{, }&b\neq \frac{x}{3}\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To find the opposite of a+3b, find the opposite of each term.

$$\left(-a-3b\right)x+3ab=0$$

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

$$-ax-3bx+3ab=0$$

Add 3bx to both sides. Anything plus zero gives itself.

$$-ax+3ab=3bx$$

Combine all terms containing a.

$$\left(-x+3b\right)a=3bx$$

The equation is in standard form.

$$\left(3b-x\right)a=3bx$$

Divide both sides by -x+3b.

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

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

$$a=\frac{3bx}{3b-x}$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

To find the opposite of a+3b, find the opposite of each term.

$$\left(-a-3b\right)x+3ab=0$$

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

$$-ax-3bx+3ab=0$$

Add ax to both sides. Anything plus zero gives itself.

$$-3bx+3ab=ax$$

Combine all terms containing b.

$$\left(-3x+3a\right)b=ax$$

The equation is in standard form.

$$\left(3a-3x\right)b=ax$$

Divide both sides by -3x+3a.

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

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

$$b=\frac{ax}{3a-3x}$$

Divide ax by -3x+3a.

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

Solve for a

$$\left\{\begin{matrix}a=\frac{3bx}{3b-x}\text{, }&b\neq \frac{x}{3}\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To find the opposite of a+3b, find the opposite of each term.

$$\left(-a-3b\right)x+3ab=0$$

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

$$-ax-3bx+3ab=0$$

Add 3bx to both sides. Anything plus zero gives itself.

$$-ax+3ab=3bx$$

Combine all terms containing a.

$$\left(-x+3b\right)a=3bx$$

The equation is in standard form.

$$\left(3b-x\right)a=3bx$$

Divide both sides by -x+3b.

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

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

$$a=\frac{3bx}{3b-x}$$

Solve for b

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

Steps for Solving Linear Equation

To find the opposite of a+3b, find the opposite of each term.

$$\left(-a-3b\right)x+3ab=0$$

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

$$-ax-3bx+3ab=0$$

Add ax to both sides. Anything plus zero gives itself.

$$-3bx+3ab=ax$$

Combine all terms containing b.

$$\left(-3x+3a\right)b=ax$$

The equation is in standard form.

$$\left(3a-3x\right)b=ax$$

Divide both sides by -3x+3a.

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

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

$$b=\frac{ax}{3a-3x}$$

Divide ax by -3x+3a.

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