Solve for p 3+12(3p+2)=9(p-3)

$3 + 12 (3 p + 2) = 9 (p - 3)$

Simplify $3 + 12 (3 p + 2)$ .

Simplify each term.

Apply the distributive property.

$3 + 12 (3 p) + 12 \cdot 2 = 9 (p - 3)$

Multiply $3$ by $12$ .

$3 + 36 p + 12 \cdot 2 = 9 (p - 3)$

Multiply $12$ by $2$ .

$3 + 36 p + 24 = 9 (p - 3)$

Add $3$ and $24$ .

$36 p + 27 = 9 (p - 3)$

Simplify $9 (p - 3)$ .

Apply the distributive property.

$36 p + 27 = 9 p + 9 \cdot - 3$

Multiply $9$ by $- 3$ .

$36 p + 27 = 9 p - 27$

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

Subtract $9 p$ from both sides of the equation.

$36 p + 27 - 9 p = - 27$

Subtract $9 p$ from $36 p$ .

$27 p + 27 = - 27$

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

Subtract $27$ from both sides of the equation.

$27 p = - 27 - 27$

Subtract $27$ from $- 27$ .

$27 p = - 54$

Divide each term in $27 p = - 54$ by $27$ and simplify.

Divide each term in $27 p = - 54$ by $27$ .

$\frac{27 p}{27} = \frac{- 54}{27}$

Simplify the left side.

Cancel the common factor of $27$ .

Cancel the common factor.

$\frac{27 p}{27} = \frac{- 54}{27}$

Divide $p$ by $1$ .

$p = \frac{- 54}{27}$

Simplify the right side.

Divide $- 54$ by $27$ .

$p = - 2$