Simplify 4 square root of 15(-3 square root of 6+5)

$4 \sqrt{15} (- 3 \sqrt{6} + 5)$

Apply the distributive property.

$4 \sqrt{15} (- 3 \sqrt{6}) + 4 \sqrt{15} \cdot 5$

Multiply $4 \sqrt{15} (- 3 \sqrt{6})$ .

Multiply $- 3$ by $4$ .

$- 12 \sqrt{15} \sqrt{6} + 4 \sqrt{15} \cdot 5$

Combine using the product rule for radicals.

$- 12 \sqrt{6 \cdot 15} + 4 \sqrt{15} \cdot 5$

Multiply $6$ by $15$ .

$- 12 \sqrt{90} + 4 \sqrt{15} \cdot 5$

Multiply $5$ by $4$ .

$- 12 \sqrt{90} + 20 \sqrt{15}$

Simplify each term.

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$- 12 \sqrt{9 (10)} + 20 \sqrt{15}$

Rewrite $9$ as $3^{2}$ .

$- 12 \sqrt{3^{2} \cdot 10} + 20 \sqrt{15}$

Pull terms out from under the radical.

$- 12 (3 \sqrt{10}) + 20 \sqrt{15}$

Multiply $3$ by $- 12$ .

$- 36 \sqrt{10} + 20 \sqrt{15}$

The result can be shown in multiple forms.

Exact Form:

$- 36 \sqrt{10} + 20 \sqrt{15}$

Decimal Form:

$- 36.38232884 \dots$