Solve for p -p-13=-4/3p+2/3(5p-6)

$- p - 13 = - \frac{4}{3} p + \frac{2}{3} (5 p - 6)$

Since $p$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- \frac{4}{3} p + \frac{2}{3} \cdot (5 p - 6) = - p - 13$

Simplify $- \frac{4}{3} p + \frac{2}{3} \cdot (5 p - 6)$ .

Simplify each term.

Combine $p$ and $\frac{4}{3}$ .

$- \frac{p \cdot 4}{3} + \frac{2}{3} \cdot (5 p - 6) = - p - 13$

Move $4$ to the left of $p$ .

$- \frac{4 \cdot p}{3} + \frac{2}{3} \cdot (5 p - 6) = - p - 13$

Apply the distributive property.

$- \frac{4 p}{3} + \frac{2}{3} (5 p) + \frac{2}{3} \cdot - 6 = - p - 13$

Multiply $\frac{2}{3} (5 p)$ .

Combine $5$ and $\frac{2}{3}$ .

$- \frac{4 p}{3} + \frac{5 \cdot 2}{3} p + \frac{2}{3} \cdot - 6 = - p - 13$

Multiply $5$ by $2$ .

$- \frac{4 p}{3} + \frac{10}{3} p + \frac{2}{3} \cdot - 6 = - p - 13$

Combine $\frac{10}{3}$ and $p$ .

$- \frac{4 p}{3} + \frac{10 p}{3} + \frac{2}{3} \cdot - 6 = - p - 13$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$- \frac{4 p}{3} + \frac{10 p}{3} + \frac{2}{3} \cdot (3 (- 2)) = - p - 13$

Cancel the common factor.

$- \frac{4 p}{3} + \frac{10 p}{3} + \frac{2}{3} \cdot (3 \cdot - 2) = - p - 13$

Rewrite the expression.

$- \frac{4 p}{3} + \frac{10 p}{3} + 2 \cdot - 2 = - p - 13$

Multiply $2$ by $- 2$ .

$- \frac{4 p}{3} + \frac{10 p}{3} - 4 = - p - 13$

Simplify terms.

Combine the numerators over the common denominator.

$- 4 + \frac{- 4 p + 10 p}{3} = - p - 13$

Add $- 4 p$ and $10 p$ .

$- 4 + \frac{6 p}{3} = - p - 13$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 p$ .

$- 4 + \frac{3 (2 p)}{3} = - p - 13$

Cancel the common factors.

Factor $3$ out of $3$ .

$- 4 + \frac{3 (2 p)}{3 (1)} = - p - 13$

Cancel the common factor.

$- 4 + \frac{3 (2 p)}{3 \cdot 1} = - p - 13$

Rewrite the expression.

$- 4 + \frac{2 p}{1} = - p - 13$

Divide $2 p$ by $1$ .

$- 4 + 2 p = - p - 13$

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

Add $p$ to both sides of the equation.

$- 4 + 2 p + p = - 13$

Add $2 p$ and $p$ .

$- 4 + 3 p = - 13$

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

Add $4$ to both sides of the equation.

$3 p = - 13 + 4$

Add $- 13$ and $4$ .

$3 p = - 9$

Divide each term in $3 p = - 9$ by $3$ and simplify.

Divide each term in $3 p = - 9$ by $3$ .

$\frac{3 p}{3} = \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 p}{3} = \frac{- 9}{3}$

Divide $p$ by $1$ .

$p = \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$p = - 3$

Solve for p -p-13=-4/3p+2/3(5p-6)

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