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

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

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

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 2$ .

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

Multiply $- 2$ by $3$ .

$7 x - 4 x - 6 = 3 (4 + x)$

Subtract $4 x$ from $7 x$ .

$3 x - 6 = 3 (4 + x)$

Simplify $3 (4 + x)$ .

Apply the distributive property.

$3 x - 6 = 3 \cdot 4 + 3 x$

Multiply $3$ by $4$ .

$3 x - 6 = 12 + 3 x$

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

Subtract $3 x$ from both sides of the equation.

$3 x - 6 - 3 x = 12$

Combine the opposite terms in $3 x - 6 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 6 = 12$

Subtract $6$ from $0$ .

$- 6 = 12$

Since $- 6 \neq 12$ , there are no solutions.

No solution