Solve for p p-5(p+4)=p-(8-p)

$p - 5 (p + 4) = p - (8 - p)$

Step 1

Simplify $p - 5 (p + 4)$ .

Simplify each term.

Apply the distributive property.

$p - 5 p - 5 \cdot 4 = p - (8 - p)$

Multiply $- 5$ by $4$ .

$p - 5 p - 20 = p - (8 - p)$

Subtract $5 p$ from $p$ .

$- 4 p - 20 = p - (8 - p)$

Step 2

Simplify $p - (8 - p)$ .

Simplify each term.

Apply the distributive property.

$- 4 p - 20 = p - 1 \cdot 8 - - p$

Multiply $- 1$ by $8$ .

$- 4 p - 20 = p - 8 - - p$

Multiply $- - p$ .

Multiply $- 1$ by $- 1$ .

$- 4 p - 20 = p - 8 + 1 p$

Multiply $p$ by $1$ .

$- 4 p - 20 = p - 8 + p$

Add $p$ and $p$ .

$- 4 p - 20 = 2 p - 8$

Step 3

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

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

$- 4 p - 20 - 2 p = - 8$

Subtract $2 p$ from $- 4 p$ .

$- 6 p - 20 = - 8$

Step 4

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

Add $20$ to both sides of the equation.

$- 6 p = - 8 + 20$

Add $- 8$ and $20$ .

$- 6 p = 12$

Step 5

Divide each term in $- 6 p = 12$ by $- 6$ and simplify.

Divide each term in $- 6 p = 12$ by $- 6$ .

$\frac{- 6 p}{- 6} = \frac{12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 p}{- 6} = \frac{12}{- 6}$

Divide $p$ by $1$ .

$p = \frac{12}{- 6}$

Simplify the right side.

Divide $12$ by $- 6$ .

$p = - 2$

Solve for p p-5(p+4)=p-(8-p)

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