Solve for u 4(u+1)+u=3(u-2)+2

$4 (u + 1) + u = 3 (u - 2) + 2$

Simplify $4 (u + 1) + u$ .

Simplify each term.

Apply the distributive property.

$4 u + 4 \cdot 1 + u = 3 (u - 2) + 2$

Multiply $4$ by $1$ .

$4 u + 4 + u = 3 (u - 2) + 2$

Add $4 u$ and $u$ .

$5 u + 4 = 3 (u - 2) + 2$

Simplify $3 (u - 2) + 2$ .

Simplify each term.

Apply the distributive property.

$5 u + 4 = 3 u + 3 \cdot - 2 + 2$

Multiply $3$ by $- 2$ .

$5 u + 4 = 3 u - 6 + 2$

Add $- 6$ and $2$ .

$5 u + 4 = 3 u - 4$

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

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

$5 u + 4 - 3 u = - 4$

Subtract $3 u$ from $5 u$ .

$2 u + 4 = - 4$

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

Subtract $4$ from both sides of the equation.

$2 u = - 4 - 4$

Subtract $4$ from $- 4$ .

$2 u = - 8$

Divide each term in $2 u = - 8$ by $2$ and simplify.

Divide each term in $2 u = - 8$ by $2$ .

$\frac{2 u}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 u}{2} = \frac{- 8}{2}$

Divide $u$ by $1$ .

$u = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$u = - 4$