Simplify -4d(5d^2-12)+7(d+5)

$- 4 d (5 d^{2} - 12) + 7 (d + 5)$

Simplify each term.

Apply the distributive property.

$- 4 d (5 d^{2}) - 4 d \cdot - 12 + 7 (d + 5)$

Rewrite using the commutative property of multiplication.

$- 4 \cdot 5 d \cdot d^{2} - 4 d \cdot - 12 + 7 (d + 5)$

Multiply $- 12$ by $- 4$ .

$- 4 \cdot 5 d \cdot d^{2} + 48 d + 7 (d + 5)$

Simplify each term.

Multiply $d$ by $d^{2}$ by adding the exponents.

Move $d^{2}$ .

$- 4 \cdot 5 (d^{2} d) + 48 d + 7 (d + 5)$

Multiply $d^{2}$ by $d$ .

Raise $d$ to the power of $1$ .

$- 4 \cdot 5 (d^{2} d^{1}) + 48 d + 7 (d + 5)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 4 \cdot 5 d^{2 + 1} + 48 d + 7 (d + 5)$

Add $2$ and $1$ .

$- 4 \cdot 5 d^{3} + 48 d + 7 (d + 5)$

Multiply $- 4$ by $5$ .

$- 20 d^{3} + 48 d + 7 (d + 5)$

Apply the distributive property.

$- 20 d^{3} + 48 d + 7 d + 7 \cdot 5$

Multiply $7$ by $5$ .

$- 20 d^{3} + 48 d + 7 d + 35$

Add $48 d$ and $7 d$ .

$- 20 d^{3} + 55 d + 35$