Solve for a (-3a-6)/2=4-5a

$\frac{- 3 a - 6}{2} = 4 - 5 a$

Step 1

Multiply both sides by $2$ .

$\frac{- 3 a - 6}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{- 3 a - 6}{2} \cdot 2$ .

Factor $3$ out of $- 3 a - 6$ .

Factor $3$ out of $- 3 a$ .

$\frac{3 (- a) - 6}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Factor $3$ out of $- 6$ .

$\frac{3 (- a) + 3 (- 2)}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Factor $3$ out of $3 (- a) + 3 (- 2)$ .

$\frac{3 (- a - 2)}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 (- a - 2)}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Rewrite the expression.

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

Apply the distributive property.

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

Multiply.

Multiply $- 1$ by $3$ .

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

Multiply $3$ by $- 2$ .

$- 3 a - 6 = (4 - 5 a) \cdot 2$

Simplify the right side.

Simplify $(4 - 5 a) \cdot 2$ .

Apply the distributive property.

$- 3 a - 6 = 4 \cdot 2 - 5 a \cdot 2$

Simplify the expression.

Multiply $4$ by $2$ .

$- 3 a - 6 = 8 - 5 a \cdot 2$

Multiply $2$ by $- 5$ .

$- 3 a - 6 = 8 - 10 a$

Reorder $8$ and $- 10 a$ .

$- 3 a - 6 = - 10 a + 8$

Step 3

Solve for $a$ .

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

Add $10 a$ to both sides of the equation.

$- 3 a - 6 + 10 a = 8$

Add $- 3 a$ and $10 a$ .

$7 a - 6 = 8$

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

Add $6$ to both sides of the equation.

$7 a = 8 + 6$

Add $8$ and $6$ .

$7 a = 14$

Divide each term in $7 a = 14$ by $7$ and simplify.

Divide each term in $7 a = 14$ by $7$ .

$\frac{7 a}{7} = \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 a}{7} = \frac{14}{7}$

Divide $a$ by $1$ .

$a = \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$a = 2$

Solve for a (-3a-6)/2=4-5a

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