Solve for a z=9a-9-3b ; for a

$z = 9 a - 9 - 3 b$ ; for $a$

Rewrite the equation as $9 a - 9 - 3 b = z$ .

$9 a - 9 - 3 b = z$

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

Add $9$ to both sides of the equation.

$9 a - 3 b = z + 9$

Add $3 b$ to both sides of the equation.

$9 a = z + 9 + 3 b$

Divide each term in $9 a = z + 9 + 3 b$ by $9$ and simplify.

Divide each term in $9 a = z + 9 + 3 b$ by $9$ .

$\frac{9 a}{9} = \frac{z}{9} + \frac{9}{9} + \frac{3 b}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 a}{9} = \frac{z}{9} + \frac{9}{9} + \frac{3 b}{9}$

Divide $a$ by $1$ .

$a = \frac{z}{9} + \frac{9}{9} + \frac{3 b}{9}$

Simplify the right side.

Simplify each term.

Divide $9$ by $9$ .

$a = \frac{z}{9} + 1 + \frac{3 b}{9}$

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3 b$ .

$a = \frac{z}{9} + 1 + \frac{3 (b)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$a = \frac{z}{9} + 1 + \frac{3 b}{3 \cdot 3}$

Cancel the common factor.

$a = \frac{z}{9} + 1 + \frac{3 b}{3 \cdot 3}$

Rewrite the expression.

$a = \frac{z}{9} + 1 + \frac{b}{3}$