Solve for a -8(-4+a)+3(2a+1)=-19

$- 8 (- 4 + a) + 3 (2 a + 1) = - 19$

Simplify $- 8 (- 4 + a) + 3 (2 a + 1)$ .

Simplify each term.

Apply the distributive property.

$- 8 \cdot - 4 - 8 a + 3 (2 a + 1) = - 19$

Multiply $- 8$ by $- 4$ .

$32 - 8 a + 3 (2 a + 1) = - 19$

Apply the distributive property.

$32 - 8 a + 3 (2 a) + 3 \cdot 1 = - 19$

Multiply $2$ by $3$ .

$32 - 8 a + 6 a + 3 \cdot 1 = - 19$

Multiply $3$ by $1$ .

$32 - 8 a + 6 a + 3 = - 19$

Simplify by adding terms.

Add $32$ and $3$ .

$- 8 a + 6 a + 35 = - 19$

Add $- 8 a$ and $6 a$ .

$- 2 a + 35 = - 19$

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

Subtract $35$ from both sides of the equation.

$- 2 a = - 19 - 35$

Subtract $35$ from $- 19$ .

$- 2 a = - 54$

Divide each term in $- 2 a = - 54$ by $- 2$ and simplify.

Divide each term in $- 2 a = - 54$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{- 54}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{- 54}{- 2}$

Divide $a$ by $1$ .

$a = \frac{- 54}{- 2}$

Simplify the right side.

Divide $- 54$ by $- 2$ .

$a = 27$