Solve for a a-b=b-a

$a - b = b - a$

Move all terms containing $a$ to the left side of the equation.

Add $a$ to both sides of the equation.

$a - b + a = b$

Add $a$ and $a$ .

$2 a - b = b$

Move all terms not containing $a$ to the right side of the equation.

Add $b$ to both sides of the equation.

$2 a = b + b$

Add $b$ and $b$ .

$2 a = 2 b$

Divide each term in $2 a = 2 b$ by $2$ and simplify.

Divide each term in $2 a = 2 b$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

$a = b$