Solve 4ax-6hx+6a=9b

$$4 a x - 6 h x + 6 a = 9 b$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Add 6hx to both sides.

$$4ax+6a=9b+6hx$$

Combine all terms containing a.

$$\left(4x+6\right)a=9b+6hx$$

The equation is in standard form.

$$\left(4x+6\right)a=6hx+9b$$

Divide both sides by 4x+6.

$$\frac{\left(4x+6\right)a}{4x+6}=\frac{6hx+9b}{4x+6}$$

Dividing by 4x+6 undoes the multiplication by 4x+6.

$$a=\frac{6hx+9b}{4x+6}$$

Divide 9b+6hx by 4x+6.

$$a=\frac{3\left(2hx+3b\right)}{2\left(2x+3\right)}$$

Solve for a

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

Steps for Solving Linear Equation

Add 6hx to both sides.

$$4ax+6a=9b+6hx$$

Combine all terms containing a.

$$\left(4x+6\right)a=9b+6hx$$

The equation is in standard form.

$$\left(4x+6\right)a=6hx+9b$$

Divide both sides by 4x+6.

$$\frac{\left(4x+6\right)a}{4x+6}=\frac{6hx+9b}{4x+6}$$

Dividing by 4x+6 undoes the multiplication by 4x+6.

$$a=\frac{6hx+9b}{4x+6}$$

Divide 9b+6hx by 4x+6.

$$a=\frac{3\left(2hx+3b\right)}{2\left(2x+3\right)}$$

Solve for b

$$b=\frac{4ax}{9}-\frac{2hx}{3}+\frac{2a}{3}$$

Steps for Solving Linear Equation

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

$$9b=4ax-6hx+6a$$

Divide both sides by 9.

$$\frac{9b}{9}=\frac{4ax-6hx+6a}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$b=\frac{4ax-6hx+6a}{9}$$

Divide 4ax-6hx+6a by 9.

$$b=\frac{4ax}{9}-\frac{2hx}{3}+\frac{2a}{3}$$