Solve for p 1+8p-4p+5=2(p-3)-2(p-2)

$1 + 8 p - 4 p + 5 = 2 (p - 3) - 2 (p - 2)$

Step 1

Simplify $1 + 8 p - 4 p + 5$ .

Add $1$ and $5$ .

$8 p - 4 p + 6 = 2 (p - 3) - 2 (p - 2)$

Subtract $4 p$ from $8 p$ .

$4 p + 6 = 2 (p - 3) - 2 (p - 2)$

Step 2

Simplify $2 (p - 3) - 2 (p - 2)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 3$ .

$4 p + 6 = 2 p - 6 - 2 (p - 2)$

Apply the distributive property.

$4 p + 6 = 2 p - 6 - 2 p - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$4 p + 6 = 2 p - 6 - 2 p + 4$

Simplify by adding terms.

Combine the opposite terms in $2 p - 6 - 2 p + 4$ .

Subtract $2 p$ from $2 p$ .

$4 p + 6 = 0 - 6 + 4$

Subtract $6$ from $0$ .

$4 p + 6 = - 6 + 4$

Add $- 6$ and $4$ .

$4 p + 6 = - 2$

Step 3

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

Subtract $6$ from both sides of the equation.

$4 p = - 2 - 6$

Subtract $6$ from $- 2$ .

$4 p = - 8$

Step 4

Divide each term in $4 p = - 8$ by $4$ and simplify.

Divide each term in $4 p = - 8$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $p$ by $1$ .

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

Simplify the right side.

Divide $- 8$ by $4$ .

$p = - 2$