Solve for k -7(k+9)=9(k-5)-14k

$- 7 (k + 9) = 9 (k - 5) - 14 k$

Since $k$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$9 (k - 5) - 14 k = - 7 (k + 9)$

Simplify $9 (k - 5) - 14 k$ .

Simplify each term.

Apply the distributive property.

$9 k + 9 \cdot - 5 - 14 k = - 7 (k + 9)$

Multiply $9$ by $- 5$ .

$9 k - 45 - 14 k = - 7 (k + 9)$

Subtract $14 k$ from $9 k$ .

$- 5 k - 45 = - 7 (k + 9)$

Simplify $- 7 (k + 9)$ .

Apply the distributive property.

$- 5 k - 45 = - 7 k - 7 \cdot 9$

Multiply $- 7$ by $9$ .

$- 5 k - 45 = - 7 k - 63$

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

Add $7 k$ to both sides of the equation.

$- 5 k - 45 + 7 k = - 63$

Add $- 5 k$ and $7 k$ .

$2 k - 45 = - 63$

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

Add $45$ to both sides of the equation.

$2 k = - 63 + 45$

Add $- 63$ and $45$ .

$2 k = - 18$

Divide each term in $2 k = - 18$ by $2$ and simplify.

Divide each term in $2 k = - 18$ by $2$ .

$\frac{2 k}{2} = \frac{- 18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 k}{2} = \frac{- 18}{2}$

Divide $k$ by $1$ .

$k = \frac{- 18}{2}$

Simplify the right side.

Divide $- 18$ by $2$ .

$k = - 9$