Solve for m -4(3m-10)-6(-7m-6)=-74

$- 4 (3 m - 10) - 6 (- 7 m - 6) = - 74$

Step 1

Simplify $- 4 (3 m - 10) - 6 (- 7 m - 6)$ .

Simplify each term.

Apply the distributive property.

$- 4 (3 m) - 4 \cdot - 10 - 6 (- 7 m - 6) = - 74$

Multiply $3$ by $- 4$ .

$- 12 m - 4 \cdot - 10 - 6 (- 7 m - 6) = - 74$

Multiply $- 4$ by $- 10$ .

$- 12 m + 40 - 6 (- 7 m - 6) = - 74$

Apply the distributive property.

$- 12 m + 40 - 6 (- 7 m) - 6 \cdot - 6 = - 74$

Multiply $- 7$ by $- 6$ .

$- 12 m + 40 + 42 m - 6 \cdot - 6 = - 74$

Multiply $- 6$ by $- 6$ .

$- 12 m + 40 + 42 m + 36 = - 74$

Simplify by adding terms.

Add $- 12 m$ and $42 m$ .

$30 m + 40 + 36 = - 74$

Add $40$ and $36$ .

$30 m + 76 = - 74$

Step 2

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

Subtract $76$ from both sides of the equation.

$30 m = - 74 - 76$

Subtract $76$ from $- 74$ .

$30 m = - 150$

Step 3

Divide each term in $30 m = - 150$ by $30$ and simplify.

Divide each term in $30 m = - 150$ by $30$ .

$\frac{30 m}{30} = \frac{- 150}{30}$

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{30 m}{30} = \frac{- 150}{30}$

Divide $m$ by $1$ .

$m = \frac{- 150}{30}$

Simplify the right side.

Divide $- 150$ by $30$ .

$m = - 5$