Solve for x 10-2(2x+1)=4(x-2)

$10 - 2 (2 x + 1) = 4 (x - 2)$

Simplify $10 - 2 (2 x + 1)$ .

Simplify each term.

Apply the distributive property.

$10 - 2 (2 x) - 2 \cdot 1 = 4 (x - 2)$

Multiply $2$ by $- 2$ .

$10 - 4 x - 2 \cdot 1 = 4 (x - 2)$

Multiply $- 2$ by $1$ .

$10 - 4 x - 2 = 4 (x - 2)$

Subtract $2$ from $10$ .

$- 4 x + 8 = 4 (x - 2)$

Simplify $4 (x - 2)$ .

Apply the distributive property.

$- 4 x + 8 = 4 x + 4 \cdot - 2$

Multiply $4$ by $- 2$ .

$- 4 x + 8 = 4 x - 8$

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

Subtract $4 x$ from both sides of the equation.

$- 4 x + 8 - 4 x = - 8$

Subtract $4 x$ from $- 4 x$ .

$- 8 x + 8 = - 8$

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

Subtract $8$ from both sides of the equation.

$- 8 x = - 8 - 8$

Subtract $8$ from $- 8$ .

$- 8 x = - 16$

Divide each term in $- 8 x = - 16$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 16$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 16}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 16}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 8}$

Simplify the right side.

Divide $- 16$ by $- 8$ .

$x = 2$