Solve for x 10x-2x+12=2(3x+5)+2x

$10 x - 2 x + 12 = 2 (3 x + 5) + 2 x$

Step 1

Subtract $2 x$ from $10 x$ .

$8 x + 12 = 2 (3 x + 5) + 2 x$

Step 2

Simplify $2 (3 x + 5) + 2 x$ .

Simplify each term.

Apply the distributive property.

$8 x + 12 = 2 (3 x) + 2 \cdot 5 + 2 x$

Multiply $3$ by $2$ .

$8 x + 12 = 6 x + 2 \cdot 5 + 2 x$

Multiply $2$ by $5$ .

$8 x + 12 = 6 x + 10 + 2 x$

Add $6 x$ and $2 x$ .

$8 x + 12 = 8 x + 10$

Step 3

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

Subtract $8 x$ from both sides of the equation.

$8 x + 12 - 8 x = 10$

Combine the opposite terms in $8 x + 12 - 8 x$ .

Subtract $8 x$ from $8 x$ .

$0 + 12 = 10$

Add $0$ and $12$ .

$12 = 10$

Step 4

Since $12 \neq 10$ , there are no solutions.

No solution