Solve for c -42=5(2c+9)-3(c+8)

$- 42 = 5 (2 c + 9) - 3 (c + 8)$

Rewrite the equation as $5 (2 c + 9) - 3 (c + 8) = - 42$ .

$5 (2 c + 9) - 3 (c + 8) = - 42$

Simplify $5 (2 c + 9) - 3 (c + 8)$ .

Simplify each term.

Apply the distributive property.

$5 (2 c) + 5 \cdot 9 - 3 (c + 8) = - 42$

Multiply $2$ by $5$ .

$10 c + 5 \cdot 9 - 3 (c + 8) = - 42$

Multiply $5$ by $9$ .

$10 c + 45 - 3 (c + 8) = - 42$

Apply the distributive property.

$10 c + 45 - 3 c - 3 \cdot 8 = - 42$

Multiply $- 3$ by $8$ .

$10 c + 45 - 3 c - 24 = - 42$

Simplify by adding terms.

Subtract $3 c$ from $10 c$ .

$7 c + 45 - 24 = - 42$

Subtract $24$ from $45$ .

$7 c + 21 = - 42$

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

Subtract $21$ from both sides of the equation.

$7 c = - 42 - 21$

Subtract $21$ from $- 42$ .

$7 c = - 63$

Divide each term in $7 c = - 63$ by $7$ and simplify.

Divide each term in $7 c = - 63$ by $7$ .

$\frac{7 c}{7} = \frac{- 63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 c}{7} = \frac{- 63}{7}$

Divide $c$ by $1$ .

$c = \frac{- 63}{7}$

Simplify the right side.

Divide $- 63$ by $7$ .

$c = - 9$