Solve for m -3(3m-10)-7=-5(m+1)+3m

$- 3 (3 m - 10) - 7 = - 5 (m + 1) + 3 m$

Since $m$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 5 (m + 1) + 3 m = - 3 (3 m - 10) - 7$

Simplify $- 5 (m + 1) + 3 m$ .

Simplify each term.

Apply the distributive property.

$- 5 m - 5 \cdot 1 + 3 m = - 3 (3 m - 10) - 7$

Multiply $- 5$ by $1$ .

$- 5 m - 5 + 3 m = - 3 (3 m - 10) - 7$

Add $- 5 m$ and $3 m$ .

$- 2 m - 5 = - 3 (3 m - 10) - 7$

Simplify $- 3 (3 m - 10) - 7$ .

Simplify each term.

Apply the distributive property.

$- 2 m - 5 = - 3 (3 m) - 3 \cdot - 10 - 7$

Multiply $3$ by $- 3$ .

$- 2 m - 5 = - 9 m - 3 \cdot - 10 - 7$

Multiply $- 3$ by $- 10$ .

$- 2 m - 5 = - 9 m + 30 - 7$

Subtract $7$ from $30$ .

$- 2 m - 5 = - 9 m + 23$

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

Add $9 m$ to both sides of the equation.

$- 2 m - 5 + 9 m = 23$

Add $- 2 m$ and $9 m$ .

$7 m - 5 = 23$

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

Add $5$ to both sides of the equation.

$7 m = 23 + 5$

Add $23$ and $5$ .

$7 m = 28$

Divide each term in $7 m = 28$ by $7$ and simplify.

Divide each term in $7 m = 28$ by $7$ .

$\frac{7 m}{7} = \frac{28}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 m}{7} = \frac{28}{7}$

Divide $m$ by $1$ .

$m = \frac{28}{7}$

Simplify the right side.

Divide $28$ by $7$ .

$m = 4$