Solve for u 4(u-2)-3u=2(u-6)

$4 (u - 2) - 3 u = 2 (u - 6)$

Step 1

Simplify $4 (u - 2) - 3 u$ .

Simplify each term.

Apply the distributive property.

$4 u + 4 \cdot - 2 - 3 u = 2 (u - 6)$

Multiply $4$ by $- 2$ .

$4 u - 8 - 3 u = 2 (u - 6)$

Subtract $3 u$ from $4 u$ .

$u - 8 = 2 (u - 6)$

Step 2

Simplify $2 (u - 6)$ .

Apply the distributive property.

$u - 8 = 2 u + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$u - 8 = 2 u - 12$

Step 3

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

Subtract $2 u$ from both sides of the equation.

$u - 8 - 2 u = - 12$

Subtract $2 u$ from $u$ .

$- u - 8 = - 12$

Step 4

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

Add $8$ to both sides of the equation.

$- u = - 12 + 8$

Add $- 12$ and $8$ .

$- u = - 4$

Step 5

Divide each term in $- u = - 4$ by $- 1$ and simplify.

Divide each term in $- u = - 4$ by $- 1$ .

$\frac{- u}{- 1} = \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{u}{1} = \frac{- 4}{- 1}$

Divide $u$ by $1$ .

$u = \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$u = 4$