Solve for x 4(3-x)+7x=4x+12+2x

$4 (3 - x) + 7 x = 4 x + 12 + 2 x$

Step 1

Simplify $4 (3 - x) + 7 x$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 3 + 4 (- x) + 7 x = 4 x + 12 + 2 x$

Multiply $4$ by $3$ .

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

Multiply $- 1$ by $4$ .

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

Add $- 4 x$ and $7 x$ .

$12 + 3 x = 4 x + 12 + 2 x$

Step 2

Add $4 x$ and $2 x$ .

$12 + 3 x = 6 x + 12$

Step 3

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

Subtract $6 x$ from both sides of the equation.

$12 + 3 x - 6 x = 12$

Subtract $6 x$ from $3 x$ .

$12 - 3 x = 12$

Step 4

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

Subtract $12$ from both sides of the equation.

$- 3 x = 12 - 12$

Subtract $12$ from $12$ .

$- 3 x = 0$

Step 5

Divide each term in $- 3 x = 0$ by $- 3$ and simplify.

Divide each term in $- 3 x = 0$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{0}{- 3}$

Divide $x$ by $1$ .

$x = \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$x = 0$