Solve a*(b-2)=3b

$$a \cdot (b-2) = 3b$$

Solve for a

$$a=\frac{3b}{b-2}$$

$$b\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by b-2.

$$ab-2a=3b$$

Combine all terms containing a.

$$\left(b-2\right)a=3b$$

Divide both sides by b-2.

$$\frac{\left(b-2\right)a}{b-2}=\frac{3b}{b-2}$$

Dividing by b-2 undoes the multiplication by b-2.

$$a=\frac{3b}{b-2}$$

Solve for b

$$b=\frac{2a}{a-3}$$

$$a\neq 3$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by b-2.

$$ab-2a=3b$$

Subtract 3b from both sides.

$$ab-2a-3b=0$$

Add 2a to both sides. Anything plus zero gives itself.

$$ab-3b=2a$$

Combine all terms containing b.

$$\left(a-3\right)b=2a$$

Divide both sides by a-3.

$$\frac{\left(a-3\right)b}{a-3}=\frac{2a}{a-3}$$

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

$$b=\frac{2a}{a-3}$$