Evaluate 3/2((58-10^2)÷( square root of 16+3))

$\frac{3}{2} ((58 - 10^{2}) \div (\sqrt{16} + 3))$

Simplify the numerator.

Raise $10$ to the power of $2$ .

$\frac{3}{2} \cdot (58 - 1 \cdot 100) \div (\sqrt{16} + 3)$

Multiply $- 1$ by $100$ .

$\frac{3}{2} \cdot (58 - 100) \div (\sqrt{16} + 3)$

Subtract $100$ from $58$ .

$\frac{3}{2} \cdot - 42 \div (\sqrt{16} + 3)$

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$\frac{3}{2} \cdot - 42 \div (\sqrt{4^{2}} + 3)$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3}{2} \cdot - 42 \div (4 + 3)$

Add $4$ and $3$ .

$\frac{3}{2} \cdot - 42 \div 7$

Reduce the expression by cancelling the common factors.

Divide $- 42$ by $7$ .

$\frac{3}{2} \cdot - 6$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$\frac{3}{2} \cdot (2 (- 3))$

Cancel the common factor.

$\frac{3}{2} \cdot (2 \cdot - 3)$

Rewrite the expression.

$3 \cdot - 3$

Multiply $3$ by $- 3$ .

$- 9$