Find All Complex Solutions 2(3x+5)=2(2x-3)+2x

$2 (3 x + 5) = 2 (2 x - 3) + 2 x$

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.

$2 (2 x - 3) + 2 x = 2 (3 x + 5)$

Step 2

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 3$ .

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

Add $4 x$ and $2 x$ .

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

Step 3

Simplify $2 (3 x + 5)$ .

Apply the distributive property.

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

Multiply.

Multiply $3$ by $2$ .

$6 x - 6 = 6 x + 2 \cdot 5$

Multiply $2$ by $5$ .

$6 x - 6 = 6 x + 10$

Step 4

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

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

$6 x - 6 - 6 x = 10$

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

Subtract $6 x$ from $6 x$ .

$0 - 6 = 10$

Subtract $6$ from $0$ .

$- 6 = 10$

Step 5

Since $- 6 \neq 10$ , there are no solutions.

No solution