Solve for n (5(n+4))/3=n-8

$\frac{5 (n + 4)}{3} = n - 8$

Step 1

Multiply both sides by $3$ .

$\frac{5 (n + 4)}{3} \cdot 3 = (n - 8) \cdot 3$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{5 (n + 4)}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5 (n + 4)}{3} \cdot 3 = (n - 8) \cdot 3$

Rewrite the expression.

$5 (n + 4) = (n - 8) \cdot 3$

Apply the distributive property.

$5 n + 5 \cdot 4 = (n - 8) \cdot 3$

Multiply $5$ by $4$ .

$5 n + 20 = (n - 8) \cdot 3$

Simplify the right side.

Simplify $(n - 8) \cdot 3$ .

Apply the distributive property.

$5 n + 20 = n \cdot 3 - 8 \cdot 3$

Simplify the expression.

Move $3$ to the left of $n$ .

$5 n + 20 = 3 \cdot n - 8 \cdot 3$

Multiply $- 8$ by $3$ .

$5 n + 20 = 3 n - 24$

Step 3

Solve for $n$ .

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

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

$5 n + 20 - 3 n = - 24$

Subtract $3 n$ from $5 n$ .

$2 n + 20 = - 24$

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

Subtract $20$ from both sides of the equation.

$2 n = - 24 - 20$

Subtract $20$ from $- 24$ .

$2 n = - 44$

Divide each term in $2 n = - 44$ by $2$ and simplify.

Divide each term in $2 n = - 44$ by $2$ .

$\frac{2 n}{2} = \frac{- 44}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{- 44}{2}$

Divide $n$ by $1$ .

$n = \frac{- 44}{2}$

Simplify the right side.

Divide $- 44$ by $2$ .

$n = - 22$

Solve for n (5(n+4))/3=n-8

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