Simplify -3(5x^2+2x+9)+x(2x-3)

$- 3 (5 x^{2} + 2 x + 9) + x (2 x - 3)$

Step 1

Simplify each term.

Apply the distributive property.

$- 3 (5 x^{2}) - 3 (2 x) - 3 \cdot 9 + x (2 x - 3)$

Simplify.

Multiply $5$ by $- 3$ .

$- 15 x^{2} - 3 (2 x) - 3 \cdot 9 + x (2 x - 3)$

Multiply $2$ by $- 3$ .

$- 15 x^{2} - 6 x - 3 \cdot 9 + x (2 x - 3)$

Multiply $- 3$ by $9$ .

$- 15 x^{2} - 6 x - 27 + x (2 x - 3)$

Apply the distributive property.

$- 15 x^{2} - 6 x - 27 + x (2 x) + x \cdot - 3$

Rewrite using the commutative property of multiplication.

$- 15 x^{2} - 6 x - 27 + 2 x \cdot x + x \cdot - 3$

Move $- 3$ to the left of $x$ .

$- 15 x^{2} - 6 x - 27 + 2 x \cdot x - 3 \cdot x$

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

Move $x$ .

$- 15 x^{2} - 6 x - 27 + 2 (x \cdot x) - 3 \cdot x$

Multiply $x$ by $x$ .

$- 15 x^{2} - 6 x - 27 + 2 x^{2} - 3 \cdot x$

$- 15 x^{2} - 6 x - 27 + 2 x^{2} - 3 x$

Step 2

Simplify by adding terms.

Add $- 15 x^{2}$ and $2 x^{2}$ .

$- 13 x^{2} - 6 x - 27 - 3 x$

Subtract $3 x$ from $- 6 x$ .

$- 13 x^{2} - 9 x - 27$