Solve for x 5(2x+4)-3(4x-6)=2(20-x)

$5 (2 x + 4) - 3 (4 x - 6) = 2 (20 - x)$

Simplify $5 (2 x + 4) - 3 (4 x - 6)$ .

Simplify each term.

Apply the distributive property.

$5 (2 x) + 5 \cdot 4 - 3 (4 x - 6) = 2 (20 - x)$

Multiply $2$ by $5$ .

$10 x + 5 \cdot 4 - 3 (4 x - 6) = 2 (20 - x)$

Multiply $5$ by $4$ .

$10 x + 20 - 3 (4 x - 6) = 2 (20 - x)$

Apply the distributive property.

$10 x + 20 - 3 (4 x) - 3 \cdot - 6 = 2 (20 - x)$

Multiply $4$ by $- 3$ .

$10 x + 20 - 12 x - 3 \cdot - 6 = 2 (20 - x)$

Multiply $- 3$ by $- 6$ .

$10 x + 20 - 12 x + 18 = 2 (20 - x)$

Simplify by adding terms.

Subtract $12 x$ from $10 x$ .

$- 2 x + 20 + 18 = 2 (20 - x)$

Add $20$ and $18$ .

$- 2 x + 38 = 2 (20 - x)$

Simplify $2 (20 - x)$ .

Apply the distributive property.

$- 2 x + 38 = 2 \cdot 20 + 2 (- x)$

Multiply.

Multiply $2$ by $20$ .

$- 2 x + 38 = 40 + 2 (- x)$

Multiply $- 1$ by $2$ .

$- 2 x + 38 = 40 - 2 x$

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

Add $2 x$ to both sides of the equation.

$- 2 x + 38 + 2 x = 40$

Combine the opposite terms in $- 2 x + 38 + 2 x$ .

Add $- 2 x$ and $2 x$ .

$0 + 38 = 40$

Add $0$ and $38$ .

$38 = 40$

Since $38 \neq 40$ , there are no solutions.

No solution