Solve for k 2-4(3+4k)=54

$2 - 4 (3 + 4 k) = 54$

Step 1

Simplify $2 - 4 (3 + 4 k)$ .

Simplify each term.

Apply the distributive property.

$2 - 4 \cdot 3 - 4 (4 k) = 54$

Multiply $- 4$ by $3$ .

$2 - 12 - 4 (4 k) = 54$

Multiply $4$ by $- 4$ .

$2 - 12 - 16 k = 54$

Subtract $12$ from $2$ .

$- 10 - 16 k = 54$

Step 2

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

Add $10$ to both sides of the equation.

$- 16 k = 54 + 10$

Add $54$ and $10$ .

$- 16 k = 64$

Step 3

Divide each term in $- 16 k = 64$ by $- 16$ and simplify.

Divide each term in $- 16 k = 64$ by $- 16$ .

$\frac{- 16 k}{- 16} = \frac{64}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 k}{- 16} = \frac{64}{- 16}$

Divide $k$ by $1$ .

$k = \frac{64}{- 16}$

Simplify the right side.

Divide $64$ by $- 16$ .

$k = - 4$