Solve for x 4(3x+6)=5(2+x)

$4 (3 x + 6) = 5 (2 + x)$

Step 1

Simplify $4 (3 x + 6)$ .

Rewrite.

$0 + 0 + 4 (3 x + 6) = 5 (2 + x)$

Simplify by adding zeros.

$4 (3 x + 6) = 5 (2 + x)$

Apply the distributive property.

$4 (3 x) + 4 \cdot 6 = 5 (2 + x)$

Multiply.

Multiply $3$ by $4$ .

$12 x + 4 \cdot 6 = 5 (2 + x)$

Multiply $4$ by $6$ .

$12 x + 24 = 5 (2 + x)$

Step 2

Simplify $5 (2 + x)$ .

Apply the distributive property.

$12 x + 24 = 5 \cdot 2 + 5 x$

Multiply $5$ by $2$ .

$12 x + 24 = 10 + 5 x$

Step 3

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

Subtract $5 x$ from both sides of the equation.

$12 x + 24 - 5 x = 10$

Subtract $5 x$ from $12 x$ .

$7 x + 24 = 10$

Step 4

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

Subtract $24$ from both sides of the equation.

$7 x = 10 - 24$

Subtract $24$ from $10$ .

$7 x = - 14$

Step 5

Divide each term in $7 x = - 14$ by $7$ and simplify.

Divide each term in $7 x = - 14$ by $7$ .

$\frac{7 x}{7} = \frac{- 14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 14}{7}$

Divide $x$ by $1$ .

$x = \frac{- 14}{7}$

Simplify the right side.

Divide $- 14$ by $7$ .

$x = - 2$