Solve for p 2/3(p+6)=4+2(p-6)

$\frac{2}{3} (p + 6) = 4 + 2 (p - 6)$

Simplify $\frac{2}{3} \cdot (p + 6)$ .

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (p + 6) = 4 + 2 (p - 6)$

Simplify by adding zeros.

$\frac{2}{3} \cdot (p + 6) = 4 + 2 (p - 6)$

Apply the distributive property.

$\frac{2}{3} p + \frac{2}{3} \cdot 6 = 4 + 2 (p - 6)$

Combine $\frac{2}{3}$ and $p$ .

$\frac{2 p}{3} + \frac{2}{3} \cdot 6 = 4 + 2 (p - 6)$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{2 p}{3} + \frac{2}{3} \cdot (3 (2)) = 4 + 2 (p - 6)$

Cancel the common factor.

$\frac{2 p}{3} + \frac{2}{3} \cdot (3 \cdot 2) = 4 + 2 (p - 6)$

Rewrite the expression.

$\frac{2 p}{3} + 2 \cdot 2 = 4 + 2 (p - 6)$

Multiply $2$ by $2$ .

$\frac{2 p}{3} + 4 = 4 + 2 (p - 6)$

Simplify $4 + 2 (p - 6)$ .

Simplify each term.

Apply the distributive property.

$\frac{2 p}{3} + 4 = 4 + 2 p + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$\frac{2 p}{3} + 4 = 4 + 2 p - 12$

Subtract $12$ from $4$ .

$\frac{2 p}{3} + 4 = 2 p - 8$

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

Subtract $2 p$ from both sides of the equation.

$\frac{2 p}{3} + 4 - 2 p = - 8$

To write $- 2 p$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 p}{3} - 2 p \cdot \frac{3}{3} + 4 = - 8$

Combine $- 2 p$ and $\frac{3}{3}$ .

$\frac{2 p}{3} + \frac{- 2 p \cdot 3}{3} + 4 = - 8$

Combine the numerators over the common denominator.

$\frac{2 p - 2 p \cdot 3}{3} + 4 = - 8$

Simplify each term.

Simplify the numerator.

Factor $2 p$ out of $2 p - 2 p \cdot 3$ .

Factor $2 p$ out of $2 p$ .

$\frac{2 p (1) - 2 p \cdot 3}{3} + 4 = - 8$

Factor $2 p$ out of $- 2 p \cdot 3$ .

$\frac{2 p (1) + 2 p (- 1 \cdot 3)}{3} + 4 = - 8$

Factor $2 p$ out of $2 p (1) + 2 p (- 1 \cdot 3)$ .

$\frac{2 p (1 - 1 \cdot 3)}{3} + 4 = - 8$

Multiply $- 1$ by $3$ .

$\frac{2 p (1 - 3)}{3} + 4 = - 8$

Subtract $3$ from $1$ .

$\frac{2 p \cdot - 2}{3} + 4 = - 8$

Multiply $- 2$ by $2$ .

$\frac{- 4 p}{3} + 4 = - 8$

Move the negative in front of the fraction.

$- \frac{4 p}{3} + 4 = - 8$

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

Subtract $4$ from both sides of the equation.

$- \frac{4 p}{3} = - 8 - 4$

Subtract $4$ from $- 8$ .

$- \frac{4 p}{3} = - 12$

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 p}{3}) = - \frac{3}{4} \cdot - 12$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{4} (- \frac{4 p}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 p}{3}) = - \frac{3}{4} \cdot - 12$

Move the leading negative in $- \frac{4 p}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 p}{3} = - \frac{3}{4} \cdot - 12$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 p}{3} = - \frac{3}{4} \cdot - 12$

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 p}{3} = - \frac{3}{4} \cdot - 12$

Rewrite the expression.

$\frac{- 1}{4} (- 4 p) = - \frac{3}{4} \cdot - 12$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 p$ .

$\frac{- 1}{4} (4 (- p)) = - \frac{3}{4} \cdot - 12$

Cancel the common factor.

$\frac{- 1}{4} (4 (- p)) = - \frac{3}{4} \cdot - 12$

Rewrite the expression.

$- - p = - \frac{3}{4} \cdot - 12$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 p = - \frac{3}{4} \cdot - 12$

Multiply $p$ by $1$ .

$p = - \frac{3}{4} \cdot - 12$

Simplify the right side.

Simplify $- \frac{3}{4} \cdot - 12$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$p = \frac{- 3}{4} \cdot - 12$

Factor $4$ out of $- 12$ .

$p = \frac{- 3}{4} \cdot (4 (- 3))$

Cancel the common factor.

$p = \frac{- 3}{4} \cdot (4 \cdot - 3)$

Rewrite the expression.

$p = - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$p = 9$

Solve for p 2/3(p+6)=4+2(p-6)

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