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

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

Step 1

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

Simplify each term.

Apply the distributive property.

$2 x - 5 x - 5 \cdot - 3 = 2 (x - 10)$

Multiply $- 5$ by $- 3$ .

$2 x - 5 x + 15 = 2 (x - 10)$

Subtract $5 x$ from $2 x$ .

$- 3 x + 15 = 2 (x - 10)$

Step 2

Simplify $2 (x - 10)$ .

Apply the distributive property.

$- 3 x + 15 = 2 x + 2 \cdot - 10$

Multiply $2$ by $- 10$ .

$- 3 x + 15 = 2 x - 20$

Step 3

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

Subtract $2 x$ from both sides of the equation.

$- 3 x + 15 - 2 x = - 20$

Subtract $2 x$ from $- 3 x$ .

$- 5 x + 15 = - 20$

Step 4

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

Subtract $15$ from both sides of the equation.

$- 5 x = - 20 - 15$

Subtract $15$ from $- 20$ .

$- 5 x = - 35$

Step 5

Divide each term in $- 5 x = - 35$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 35$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 35}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 35}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 35}{- 5}$

Simplify the right side.

Divide $- 35$ by $- 5$ .

$x = 7$