Solve for a 4(2a+3)=-3(a-1)+31

$4 (2 a + 3) = - 3 (a - 1) + 31$

Simplify $4 (2 a + 3)$ .

Rewrite.

$0 + 0 + 4 (2 a + 3) = - 3 (a - 1) + 31$

Simplify by adding zeros.

$4 (2 a + 3) = - 3 (a - 1) + 31$

Apply the distributive property.

$4 (2 a) + 4 \cdot 3 = - 3 (a - 1) + 31$

Multiply.

Multiply $2$ by $4$ .

$8 a + 4 \cdot 3 = - 3 (a - 1) + 31$

Multiply $4$ by $3$ .

$8 a + 12 = - 3 (a - 1) + 31$

Simplify $- 3 (a - 1) + 31$ .

Simplify each term.

Apply the distributive property.

$8 a + 12 = - 3 a - 3 \cdot - 1 + 31$

Multiply $- 3$ by $- 1$ .

$8 a + 12 = - 3 a + 3 + 31$

Add $3$ and $31$ .

$8 a + 12 = - 3 a + 34$

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

Add $3 a$ to both sides of the equation.

$8 a + 12 + 3 a = 34$

Add $8 a$ and $3 a$ .

$11 a + 12 = 34$

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

Subtract $12$ from both sides of the equation.

$11 a = 34 - 12$

Subtract $12$ from $34$ .

$11 a = 22$

Divide each term in $11 a = 22$ by $11$ and simplify.

Divide each term in $11 a = 22$ by $11$ .

$\frac{11 a}{11} = \frac{22}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 a}{11} = \frac{22}{11}$

Divide $a$ by $1$ .

$a = \frac{22}{11}$

Simplify the right side.

Divide $22$ by $11$ .

$a = 2$