Solve for k 4k+7(-4-2k)=-2(k-2)

$4 k + 7 (- 4 - 2 k) = - 2 (k - 2)$

Simplify $4 k + 7 (- 4 - 2 k)$ .

Simplify each term.

Apply the distributive property.

$4 k + 7 \cdot - 4 + 7 (- 2 k) = - 2 (k - 2)$

Multiply $7$ by $- 4$ .

$4 k - 28 + 7 (- 2 k) = - 2 (k - 2)$

Multiply $- 2$ by $7$ .

$4 k - 28 - 14 k = - 2 (k - 2)$

Subtract $14 k$ from $4 k$ .

$- 10 k - 28 = - 2 (k - 2)$

Simplify $- 2 (k - 2)$ .

Apply the distributive property.

$- 10 k - 28 = - 2 k - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$- 10 k - 28 = - 2 k + 4$

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

Add $2 k$ to both sides of the equation.

$- 10 k - 28 + 2 k = 4$

Add $- 10 k$ and $2 k$ .

$- 8 k - 28 = 4$

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

Add $28$ to both sides of the equation.

$- 8 k = 4 + 28$

Add $4$ and $28$ .

$- 8 k = 32$

Divide each term in $- 8 k = 32$ by $- 8$ and simplify.

Divide each term in $- 8 k = 32$ by $- 8$ .

$\frac{- 8 k}{- 8} = \frac{32}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 k}{- 8} = \frac{32}{- 8}$

Divide $k$ by $1$ .

$k = \frac{32}{- 8}$

Simplify the right side.

Divide $32$ by $- 8$ .

$k = - 4$