Solve 3ax=2bx+b

$$3 a x = 2 b x + b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{2b}{3}+\frac{b}{3x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$3xa=2bx+b$$

Divide both sides by 3x.

$$\frac{3xa}{3x}=\frac{2bx+b}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$a=\frac{2bx+b}{3x}$$

Divide 2bx+b by 3x.

$$a=\frac{2b}{3}+\frac{b}{3x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{3ax}{2x+1}\text{, }&x\neq -\frac{1}{2}\\b\in \mathrm{C}\text{, }&a=0\text{ and }x=-\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2bx+b=3ax$$

Combine all terms containing b.

$$\left(2x+1\right)b=3ax$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)b}{2x+1}=\frac{3ax}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$b=\frac{3ax}{2x+1}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{2b}{3}+\frac{b}{3x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$3xa=2bx+b$$

Divide both sides by 3x.

$$\frac{3xa}{3x}=\frac{2bx+b}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$a=\frac{2bx+b}{3x}$$

Divide 2bx+b by 3x.

$$a=\frac{2b}{3}+\frac{b}{3x}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{3ax}{2x+1}\text{, }&x\neq -\frac{1}{2}\\b\in \mathrm{R}\text{, }&a=0\text{ and }x=-\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2bx+b=3ax$$

Combine all terms containing b.

$$\left(2x+1\right)b=3ax$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)b}{2x+1}=\frac{3ax}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$b=\frac{3ax}{2x+1}$$