Simplify -5(3x^2-2x+2)-3x(4x-5)

$- 5 (3 x^{2} - 2 x + 2) - 3 x (4 x - 5)$

Step 1

Simplify each term.

Apply the distributive property.

$- 5 (3 x^{2}) - 5 (- 2 x) - 5 \cdot 2 - 3 x (4 x - 5)$

Simplify.

Multiply $3$ by $- 5$ .

$- 15 x^{2} - 5 (- 2 x) - 5 \cdot 2 - 3 x (4 x - 5)$

Multiply $- 2$ by $- 5$ .

$- 15 x^{2} + 10 x - 5 \cdot 2 - 3 x (4 x - 5)$

Multiply $- 5$ by $2$ .

$- 15 x^{2} + 10 x - 10 - 3 x (4 x - 5)$

Apply the distributive property.

$- 15 x^{2} + 10 x - 10 - 3 x (4 x) - 3 x \cdot - 5$

Rewrite using the commutative property of multiplication.

$- 15 x^{2} + 10 x - 10 - 3 \cdot 4 x \cdot x - 3 x \cdot - 5$

Multiply $- 5$ by $- 3$ .

$- 15 x^{2} + 10 x - 10 - 3 \cdot 4 x \cdot x + 15 x$

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 15 x^{2} + 10 x - 10 - 3 \cdot 4 (x \cdot x) + 15 x$

Multiply $x$ by $x$ .

$- 15 x^{2} + 10 x - 10 - 3 \cdot 4 x^{2} + 15 x$

Multiply $- 3$ by $4$ .

$- 15 x^{2} + 10 x - 10 - 12 x^{2} + 15 x$

Step 2

Simplify by adding terms.

Subtract $12 x^{2}$ from $- 15 x^{2}$ .

$- 27 x^{2} + 10 x - 10 + 15 x$

Add $10 x$ and $15 x$ .

$- 27 x^{2} + 25 x - 10$