Solve for a 5-2(4a+1)+3a=13

$5 - 2 (4 a + 1) + 3 a = 13$

Step 1

Simplify $5 - 2 (4 a + 1) + 3 a$ .

Simplify each term.

Apply the distributive property.

$5 - 2 (4 a) - 2 \cdot 1 + 3 a = 13$

Multiply $4$ by $- 2$ .

$5 - 8 a - 2 \cdot 1 + 3 a = 13$

Multiply $- 2$ by $1$ .

$5 - 8 a - 2 + 3 a = 13$

Simplify by adding terms.

Subtract $2$ from $5$ .

$- 8 a + 3 + 3 a = 13$

Add $- 8 a$ and $3 a$ .

$- 5 a + 3 = 13$

Step 2

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

Subtract $3$ from both sides of the equation.

$- 5 a = 13 - 3$

Subtract $3$ from $13$ .

$- 5 a = 10$

Step 3

Divide each term in $- 5 a = 10$ by $- 5$ and simplify.

Divide each term in $- 5 a = 10$ by $- 5$ .

$\frac{- 5 a}{- 5} = \frac{10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 a}{- 5} = \frac{10}{- 5}$

Divide $a$ by $1$ .

$a = \frac{10}{- 5}$

Simplify the right side.

Divide $10$ by $- 5$ .

$a = - 2$