Solve for n 6-4(6n+7)=122

$6 - 4 (6 n + 7) = 122$

Step 1

Simplify $6 - 4 (6 n + 7)$ .

Simplify each term.

Apply the distributive property.

$6 - 4 (6 n) - 4 \cdot 7 = 122$

Multiply $6$ by $- 4$ .

$6 - 24 n - 4 \cdot 7 = 122$

Multiply $- 4$ by $7$ .

$6 - 24 n - 28 = 122$

Subtract $28$ from $6$ .

$- 24 n - 22 = 122$

Step 2

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

Add $22$ to both sides of the equation.

$- 24 n = 122 + 22$

Add $122$ and $22$ .

$- 24 n = 144$

Step 3

Divide each term in $- 24 n = 144$ by $- 24$ and simplify.

Divide each term in $- 24 n = 144$ by $- 24$ .

$\frac{- 24 n}{- 24} = \frac{144}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 n}{- 24} = \frac{144}{- 24}$

Divide $n$ by $1$ .

$n = \frac{144}{- 24}$

Simplify the right side.

Divide $144$ by $- 24$ .

$n = - 6$