Solve for A A=(-2(9-3)-3(-2+4))/(6-(5-3))+3/2

$A = \frac{- 2 (9 - 3) - 3 (- 2 + 4)}{6 - (5 - 3)} + \frac{3}{2}$

Simplify the expression.

Subtract $3$ from $9$ .

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

Add $- 2$ and $4$ .

$A = \frac{- 2 \cdot 6 - 3 \cdot 2}{6 - (5 - 3)} + \frac{3}{2}$

Multiply $- 2$ by $6$ .

$A = \frac{- 12 - 3 \cdot 2}{6 - (5 - 3)} + \frac{3}{2}$

Multiply $- 3$ by $2$ .

$A = \frac{- 12 - 6}{6 - (5 - 3)} + \frac{3}{2}$

Subtract $6$ from $- 12$ .

$A = \frac{- 18}{6 - (5 - 3)} + \frac{3}{2}$

Simplify each term.

Simplify the denominator.

Subtract $3$ from $5$ .

$A = \frac{- 18}{6 - 1 \cdot 2} + \frac{3}{2}$

Multiply $- 1$ by $2$ .

$A = \frac{- 18}{6 - 2} + \frac{3}{2}$

Subtract $2$ from $6$ .

$A = \frac{- 18}{4} + \frac{3}{2}$

Cancel the common factor of $- 18$ and $4$ .

Factor $2$ out of $- 18$ .

$A = \frac{2 (- 9)}{4} + \frac{3}{2}$

Cancel the common factors.

Factor $2$ out of $4$ .

$A = \frac{2 \cdot - 9}{2 \cdot 2} + \frac{3}{2}$

Cancel the common factor.

$A = \frac{2 \cdot - 9}{2 \cdot 2} + \frac{3}{2}$

Rewrite the expression.

$A = \frac{- 9}{2} + \frac{3}{2}$

Move the negative in front of the fraction.

$A = - \frac{9}{2} + \frac{3}{2}$

Combine fractions.

Combine the numerators over the common denominator.

$A = \frac{- 9 + 3}{2}$

Simplify the expression.

Add $- 9$ and $3$ .

$A = \frac{- 6}{2}$

Divide $- 6$ by $2$ .

$A = - 3$