Solve for a 5(a+4)-6a+1=12

$5 (a + 4) - 6 a + 1 = 12$

Simplify $5 (a + 4) - 6 a + 1$ .

Simplify each term.

Apply the distributive property.

$5 a + 5 \cdot 4 - 6 a + 1 = 12$

Multiply $5$ by $4$ .

$5 a + 20 - 6 a + 1 = 12$

Simplify by adding terms.

Subtract $6 a$ from $5 a$ .

$- a + 20 + 1 = 12$

Add $20$ and $1$ .

$- a + 21 = 12$

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

Subtract $21$ from both sides of the equation.

$- a = 12 - 21$

Subtract $21$ from $12$ .

$- a = - 9$

Divide each term in $- a = - 9$ by $- 1$ and simplify.

Divide each term in $- a = - 9$ by $- 1$ .

$\frac{- a}{- 1} = \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{- 9}{- 1}$

Divide $a$ by $1$ .

$a = \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$a = 9$