Solve for x 2(x-4)=4x+3x+12

$2 (x - 4) = 4 x + 3 x + 12$

Step 1

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

$4 x + 3 x + 12 = 2 (x - 4)$

Step 2

Add $4 x$ and $3 x$ .

$7 x + 12 = 2 (x - 4)$

Step 3

Simplify $2 (x - 4)$ .

Apply the distributive property.

$7 x + 12 = 2 x + 2 \cdot - 4$

Multiply $2$ by $- 4$ .

$7 x + 12 = 2 x - 8$

Step 4

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

Subtract $2 x$ from both sides of the equation.

$7 x + 12 - 2 x = - 8$

Subtract $2 x$ from $7 x$ .

$5 x + 12 = - 8$

Step 5

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

Subtract $12$ from both sides of the equation.

$5 x = - 8 - 12$

Subtract $12$ from $- 8$ .

$5 x = - 20$

Step 6

Divide each term in $5 x = - 20$ by $5$ and simplify.

Divide each term in $5 x = - 20$ by $5$ .

$\frac{5 x}{5} = \frac{- 20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 20}{5}$

Divide $x$ by $1$ .

$x = \frac{- 20}{5}$

Simplify the right side.

Divide $- 20$ by $5$ .

$x = - 4$