Solve for x 10(x-3)=5(3x-8)

$10 (x - 3) = 5 (3 x - 8)$

Step 1

Simplify $10 (x - 3)$ .

Rewrite.

$0 + 0 + 10 (x - 3) = 5 (3 x - 8)$

Simplify by adding zeros.

$10 (x - 3) = 5 (3 x - 8)$

Apply the distributive property.

$10 x + 10 \cdot - 3 = 5 (3 x - 8)$

Multiply $10$ by $- 3$ .

$10 x - 30 = 5 (3 x - 8)$

Step 2

Simplify $5 (3 x - 8)$ .

Apply the distributive property.

$10 x - 30 = 5 (3 x) + 5 \cdot - 8$

Multiply.

Multiply $3$ by $5$ .

$10 x - 30 = 15 x + 5 \cdot - 8$

Multiply $5$ by $- 8$ .

$10 x - 30 = 15 x - 40$

Step 3

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

Subtract $15 x$ from both sides of the equation.

$10 x - 30 - 15 x = - 40$

Subtract $15 x$ from $10 x$ .

$- 5 x - 30 = - 40$

Step 4

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

Add $30$ to both sides of the equation.

$- 5 x = - 40 + 30$

Add $- 40$ and $30$ .

$- 5 x = - 10$

Step 5

Divide each term in $- 5 x = - 10$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 10$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 5}$

Simplify the right side.

Divide $- 10$ by $- 5$ .

$x = 2$