Solve 2(a-3)+b(3-a)=2a

$$2 ( a - 3 ) + b ( 3 - a ) = 2 a$$

Solve for a

$$a=3-\frac{6}{b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by a-3.

$$2a-6+b\left(3-a\right)=2a$$

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

$$2a-6+3b-ba=2a$$

Subtract 2a from both sides.

$$2a-6+3b-ba-2a=0$$

Combine 2a and -2a to get 0.

$$-6+3b-ba=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$3b-ba=6$$

Subtract 3b from both sides.

$$-ba=6-3b$$

The equation is in standard form.

$$\left(-b\right)a=6-3b$$

Divide both sides by -b.

$$\frac{\left(-b\right)a}{-b}=\frac{6-3b}{-b}$$

Dividing by -b undoes the multiplication by -b.

$$a=\frac{6-3b}{-b}$$

Divide 6-3b by -b.

$$a=3-\frac{6}{b}$$

Solve for b

$$b=\frac{6}{3-a}$$

$$a\neq 3$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by a-3.

$$2a-6+b\left(3-a\right)=2a$$

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

$$2a-6+3b-ba=2a$$

Subtract 2a from both sides.

$$-6+3b-ba=2a-2a$$

Combine 2a and -2a to get 0.

$$-6+3b-ba=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$3b-ba=6$$

Combine all terms containing b.

$$\left(3-a\right)b=6$$

Divide both sides by 3-a.

$$\frac{\left(3-a\right)b}{3-a}=\frac{6}{3-a}$$

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

$$b=\frac{6}{3-a}$$