Solve for x 2(x+7)+3(x+12)=10

$2 (x + 7) + 3 (x + 12) = 10$

Step 1

Simplify $2 (x + 7) + 3 (x + 12)$ .

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot 7 + 3 (x + 12) = 10$

Multiply $2$ by $7$ .

$2 x + 14 + 3 (x + 12) = 10$

Apply the distributive property.

$2 x + 14 + 3 x + 3 \cdot 12 = 10$

Multiply $3$ by $12$ .

$2 x + 14 + 3 x + 36 = 10$

Simplify by adding terms.

Add $2 x$ and $3 x$ .

$5 x + 14 + 36 = 10$

Add $14$ and $36$ .

$5 x + 50 = 10$

Step 2

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

Subtract $50$ from both sides of the equation.

$5 x = 10 - 50$

Subtract $50$ from $10$ .

$5 x = - 40$

Step 3

Divide each term in $5 x = - 40$ by $5$ and simplify.

Divide each term in $5 x = - 40$ by $5$ .

$\frac{5 x}{5} = \frac{- 40}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 40}{5}$

Divide $x$ by $1$ .

$x = \frac{- 40}{5}$

Simplify the right side.

Divide $- 40$ by $5$ .

$x = - 8$