Solve for a -2(3a-2)=13(7-3a)

$- 2 (3 a - 2) = 13 (7 - 3 a)$

Simplify $- 2 (3 a - 2)$ .

Start simplifying.

$0 + 0 - 2 (3 a - 2) = 13 (7 - 3 a)$

Simplify by adding zeros.

$- 2 (3 a - 2) = 13 (7 - 3 a)$

Apply the distributive property.

$- 2 (3 a) - 2 \cdot - 2 = 13 (7 - 3 a)$

Multiply.

Multiply $3$ by $- 2$ .

$- 6 a - 2 \cdot - 2 = 13 (7 - 3 a)$

Multiply $- 2$ by $- 2$ .

$- 6 a + 4 = 13 (7 - 3 a)$

Simplify $13 (7 - 3 a)$ .

Apply the distributive property.

$- 6 a + 4 = 13 \cdot 7 + 13 (- 3 a)$

Multiply.

Multiply $13$ by $7$ .

$- 6 a + 4 = 91 + 13 (- 3 a)$

Multiply $- 3$ by $13$ .

$- 6 a + 4 = 91 - 39 a$

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

Add $39 a$ to both sides of the equation.

$- 6 a + 4 + 39 a = 91$

Add $- 6 a$ and $39 a$ .

$33 a + 4 = 91$

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

Subtract $4$ from both sides of the equation.

$33 a = 91 - 4$

Subtract $4$ from $91$ .

$33 a = 87$

Divide each term in $33 a = 87$ by $33$ and simplify.

Divide each term in $33 a = 87$ by $33$ .

$\frac{33 a}{33} = \frac{87}{33}$

Simplify the left side.

Cancel the common factor of $33$ .

Cancel the common factor.

$\frac{33 a}{33} = \frac{87}{33}$

Divide $a$ by $1$ .

$a = \frac{87}{33}$

Simplify the right side.

Cancel the common factor of $87$ and $33$ .

Factor $3$ out of $87$ .

$a = \frac{3 (29)}{33}$

Cancel the common factors.

Factor $3$ out of $33$ .

$a = \frac{3 \cdot 29}{3 \cdot 11}$

Cancel the common factor.

$a = \frac{3 \cdot 29}{3 \cdot 11}$

Rewrite the expression.

$a = \frac{29}{11}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{29}{11}$

Decimal Form:

$a = 2.\overline{63}$

Mixed Number Form:

$a = 2 \frac{7}{11}$

Solve for a -2(3a-2)=13(7-3a)

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