Solve for x 3(x+5)=5(2x-6)+3

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

Simplify $3 (x + 5)$ .

Rewrite.

$0 + 0 + 3 (x + 5) = 5 (2 x - 6) + 3$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $3$ by $5$ .

$3 x + 15 = 5 (2 x - 6) + 3$

Simplify $5 (2 x - 6) + 3$ .

Simplify each term.

Apply the distributive property.

$3 x + 15 = 5 (2 x) + 5 \cdot - 6 + 3$

Multiply $2$ by $5$ .

$3 x + 15 = 10 x + 5 \cdot - 6 + 3$

Multiply $5$ by $- 6$ .

$3 x + 15 = 10 x - 30 + 3$

Add $- 30$ and $3$ .

$3 x + 15 = 10 x - 27$

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

Subtract $10 x$ from both sides of the equation.

$3 x + 15 - 10 x = - 27$

Subtract $10 x$ from $3 x$ .

$- 7 x + 15 = - 27$

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

Subtract $15$ from both sides of the equation.

$- 7 x = - 27 - 15$

Subtract $15$ from $- 27$ .

$- 7 x = - 42$

Divide each term in $- 7 x = - 42$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 42$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 42}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 42}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 42}{- 7}$

Simplify the right side.

Divide $- 42$ by $- 7$ .

$x = 6$