Solve for n 3n-5=-8(6+5n)

$3 n - 5 = - 8 (6 + 5 n)$

Step 1

Simplify $- 8 (6 + 5 n)$ .

Rewrite.

$3 n - 5 = 0 + 0 - 8 (6 + 5 n)$

Simplify by adding zeros.

$3 n - 5 = - 8 (6 + 5 n)$

Apply the distributive property.

$3 n - 5 = - 8 \cdot 6 - 8 (5 n)$

Multiply.

Multiply $- 8$ by $6$ .

$3 n - 5 = - 48 - 8 (5 n)$

Multiply $5$ by $- 8$ .

$3 n - 5 = - 48 - 40 n$

Step 2

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

Add $40 n$ to both sides of the equation.

$3 n - 5 + 40 n = - 48$

Add $3 n$ and $40 n$ .

$43 n - 5 = - 48$

Step 3

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

Add $5$ to both sides of the equation.

$43 n = - 48 + 5$

Add $- 48$ and $5$ .

$43 n = - 43$

Step 4

Divide each term in $43 n = - 43$ by $43$ and simplify.

Divide each term in $43 n = - 43$ by $43$ .

$\frac{43 n}{43} = \frac{- 43}{43}$

Simplify the left side.

Cancel the common factor of $43$ .

Cancel the common factor.

$\frac{43 n}{43} = \frac{- 43}{43}$

Divide $n$ by $1$ .

$n = \frac{- 43}{43}$

Simplify the right side.

Divide $- 43$ by $43$ .

$n = - 1$