Solve for p 3p-16=4(p-5)+p+4

$3 p - 16 = 4 (p - 5) + p + 4$

Step 1

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

$4 (p - 5) + p + 4 = 3 p - 16$

Step 2

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

Simplify each term.

Apply the distributive property.

$4 p + 4 \cdot - 5 + p + 4 = 3 p - 16$

Multiply $4$ by $- 5$ .

$4 p - 20 + p + 4 = 3 p - 16$

Simplify by adding terms.

Add $4 p$ and $p$ .

$5 p - 20 + 4 = 3 p - 16$

Add $- 20$ and $4$ .

$5 p - 16 = 3 p - 16$

Step 3

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

Subtract $3 p$ from both sides of the equation.

$5 p - 16 - 3 p = - 16$

Subtract $3 p$ from $5 p$ .

$2 p - 16 = - 16$

Step 4

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

Add $16$ to both sides of the equation.

$2 p = - 16 + 16$

Add $- 16$ and $16$ .

$2 p = 0$

Step 5

Divide each term in $2 p = 0$ by $2$ and simplify.

Divide each term in $2 p = 0$ by $2$ .

$\frac{2 p}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 p}{2} = \frac{0}{2}$

Divide $p$ by $1$ .

$p = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$p = 0$