Solve for c 2/3(6c-18)+3/4(8c+32)=-18

$\frac{2}{3} (6 c - 18) + \frac{3}{4} (8 c + 32) = - 18$

Step 1

Simplify $\frac{2}{3} \cdot (6 c - 18) + \frac{3}{4} \cdot (8 c + 32)$ .

Simplify each term.

Apply the distributive property.

$\frac{2}{3} (6 c) + \frac{2}{3} \cdot - 18 + \frac{3}{4} \cdot (8 c + 32) = - 18$

Cancel the common factor of $3$ .

Factor $3$ out of $6 c$ .

$\frac{2}{3} (3 (2 c)) + \frac{2}{3} \cdot - 18 + \frac{3}{4} \cdot (8 c + 32) = - 18$

Cancel the common factor.

$\frac{2}{3} (3 (2 c)) + \frac{2}{3} \cdot - 18 + \frac{3}{4} \cdot (8 c + 32) = - 18$

Rewrite the expression.

$2 (2 c) + \frac{2}{3} \cdot - 18 + \frac{3}{4} \cdot (8 c + 32) = - 18$

Multiply $2$ by $2$ .

$4 c + \frac{2}{3} \cdot - 18 + \frac{3}{4} \cdot (8 c + 32) = - 18$

Cancel the common factor of $3$ .

Factor $3$ out of $- 18$ .

$4 c + \frac{2}{3} \cdot (3 (- 6)) + \frac{3}{4} \cdot (8 c + 32) = - 18$

Cancel the common factor.

$4 c + \frac{2}{3} \cdot (3 \cdot - 6) + \frac{3}{4} \cdot (8 c + 32) = - 18$

Rewrite the expression.

$4 c + 2 \cdot - 6 + \frac{3}{4} \cdot (8 c + 32) = - 18$

Multiply $2$ by $- 6$ .

$4 c - 12 + \frac{3}{4} \cdot (8 c + 32) = - 18$

Apply the distributive property.

$4 c - 12 + \frac{3}{4} (8 c) + \frac{3}{4} \cdot 32 = - 18$

Cancel the common factor of $4$ .

Factor $4$ out of $8 c$ .

$4 c - 12 + \frac{3}{4} (4 (2 c)) + \frac{3}{4} \cdot 32 = - 18$

Cancel the common factor.

$4 c - 12 + \frac{3}{4} (4 (2 c)) + \frac{3}{4} \cdot 32 = - 18$

Rewrite the expression.

$4 c - 12 + 3 (2 c) + \frac{3}{4} \cdot 32 = - 18$

Multiply $2$ by $3$ .

$4 c - 12 + 6 c + \frac{3}{4} \cdot 32 = - 18$

Cancel the common factor of $4$ .

Factor $4$ out of $32$ .

$4 c - 12 + 6 c + \frac{3}{4} \cdot (4 (8)) = - 18$

Cancel the common factor.

$4 c - 12 + 6 c + \frac{3}{4} \cdot (4 \cdot 8) = - 18$

Rewrite the expression.

$4 c - 12 + 6 c + 3 \cdot 8 = - 18$

Multiply $3$ by $8$ .

$4 c - 12 + 6 c + 24 = - 18$

Simplify by adding terms.

Add $4 c$ and $6 c$ .

$10 c - 12 + 24 = - 18$

Add $- 12$ and $24$ .

$10 c + 12 = - 18$

Step 2

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

Subtract $12$ from both sides of the equation.

$10 c = - 18 - 12$

Subtract $12$ from $- 18$ .

$10 c = - 30$

Step 3

Divide each term in $10 c = - 30$ by $10$ and simplify.

Divide each term in $10 c = - 30$ by $10$ .

$\frac{10 c}{10} = \frac{- 30}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 c}{10} = \frac{- 30}{10}$

Divide $c$ by $1$ .

$c = \frac{- 30}{10}$

Simplify the right side.

Divide $- 30$ by $10$ .

$c = - 3$

Solve for c 2/3(6c-18)+3/4(8c+32)=-18

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