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

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

Simplify $4 (2 a + 2)$ .

Start simplifying.

$0 + 0 + 4 (2 a + 2) = 8 (2 - 3 a)$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $2$ by $4$ .

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

Multiply $4$ by $2$ .

$8 a + 8 = 8 (2 - 3 a)$

Simplify $8 (2 - 3 a)$ .

Apply the distributive property.

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

Multiply.

Multiply $8$ by $2$ .

$8 a + 8 = 16 + 8 (- 3 a)$

Multiply $- 3$ by $8$ .

$8 a + 8 = 16 - 24 a$

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

Add $24 a$ to both sides of the equation.

$8 a + 8 + 24 a = 16$

Add $8 a$ and $24 a$ .

$32 a + 8 = 16$

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

Subtract $8$ from both sides of the equation.

$32 a = 16 - 8$

Subtract $8$ from $16$ .

$32 a = 8$

Divide each term in $32 a = 8$ by $32$ and simplify.

Divide each term in $32 a = 8$ by $32$ .

$\frac{32 a}{32} = \frac{8}{32}$

Simplify the left side.

Cancel the common factor of $32$ .

Cancel the common factor.

$\frac{32 a}{32} = \frac{8}{32}$

Divide $a$ by $1$ .

$a = \frac{8}{32}$

Simplify the right side.

Cancel the common factor of $8$ and $32$ .

Factor $8$ out of $8$ .

$a = \frac{8 (1)}{32}$

Cancel the common factors.

Factor $8$ out of $32$ .

$a = \frac{8 \cdot 1}{8 \cdot 4}$

Cancel the common factor.

$a = \frac{8 \cdot 1}{8 \cdot 4}$

Rewrite the expression.

$a = \frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{4}$

Decimal Form:

$a = 0.25$

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

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