Solve for u 14+8(u+12)=2(6u+19)

$14 + 8 (u + 12) = 2 (6 u + 19)$

Step 1

Simplify $14 + 8 (u + 12)$ .

Simplify each term.

Apply the distributive property.

$14 + 8 u + 8 \cdot 12 = 2 (6 u + 19)$

Multiply $8$ by $12$ .

$14 + 8 u + 96 = 2 (6 u + 19)$

Add $14$ and $96$ .

$8 u + 110 = 2 (6 u + 19)$

Step 2

Simplify $2 (6 u + 19)$ .

Apply the distributive property.

$8 u + 110 = 2 (6 u) + 2 \cdot 19$

Multiply.

Multiply $6$ by $2$ .

$8 u + 110 = 12 u + 2 \cdot 19$

Multiply $2$ by $19$ .

$8 u + 110 = 12 u + 38$

Step 3

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

Subtract $12 u$ from both sides of the equation.

$8 u + 110 - 12 u = 38$

Subtract $12 u$ from $8 u$ .

$- 4 u + 110 = 38$

Step 4

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

Subtract $110$ from both sides of the equation.

$- 4 u = 38 - 110$

Subtract $110$ from $38$ .

$- 4 u = - 72$

Step 5

Divide each term in $- 4 u = - 72$ by $- 4$ and simplify.

Divide each term in $- 4 u = - 72$ by $- 4$ .

$\frac{- 4 u}{- 4} = \frac{- 72}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 u}{- 4} = \frac{- 72}{- 4}$

Divide $u$ by $1$ .

$u = \frac{- 72}{- 4}$

Simplify the right side.

Divide $- 72$ by $- 4$ .

$u = 18$