Solve for a -4a+9=-2(4+5a)-7

$- 4 a + 9 = - 2 (4 + 5 a) - 7$

Simplify $- 2 (4 + 5 a) - 7$ .

Simplify each term.

Apply the distributive property.

$- 4 a + 9 = - 2 \cdot 4 - 2 (5 a) - 7$

Multiply $- 2$ by $4$ .

$- 4 a + 9 = - 8 - 2 (5 a) - 7$

Multiply $5$ by $- 2$ .

$- 4 a + 9 = - 8 - 10 a - 7$

Subtract $7$ from $- 8$ .

$- 4 a + 9 = - 10 a - 15$

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

Add $10 a$ to both sides of the equation.

$- 4 a + 9 + 10 a = - 15$

Add $- 4 a$ and $10 a$ .

$6 a + 9 = - 15$

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

Subtract $9$ from both sides of the equation.

$6 a = - 15 - 9$

Subtract $9$ from $- 15$ .

$6 a = - 24$

Divide each term in $6 a = - 24$ by $6$ and simplify.

Divide each term in $6 a = - 24$ by $6$ .

$\frac{6 a}{6} = \frac{- 24}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 a}{6} = \frac{- 24}{6}$

Divide $a$ by $1$ .

$a = \frac{- 24}{6}$

Simplify the right side.

Divide $- 24$ by $6$ .

$a = - 4$