Find the Product (5x^2-4x+6)(-2x+3)

$(5 x^{2} - 4 x + 6) (- 2 x + 3)$

Expand $(5 x^{2} - 4 x + 6) (- 2 x + 3)$ by multiplying each term in the first expression by each term in the second expression.

$5 x^{2} (- 2 x) + 5 x^{2} \cdot 3 - 4 x (- 2 x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot - 2 x^{2} x + 5 x^{2} \cdot 3 - 4 x (- 2 x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

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

Move $x$ .

$5 \cdot - 2 (x \cdot x^{2}) + 5 x^{2} \cdot 3 - 4 x (- 2 x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

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

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

$5 \cdot - 2 (x^{1} x^{2}) + 5 x^{2} \cdot 3 - 4 x (- 2 x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

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

$5 \cdot - 2 x^{1 + 2} + 5 x^{2} \cdot 3 - 4 x (- 2 x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

Add $1$ and $2$ .

$5 \cdot - 2 x^{3} + 5 x^{2} \cdot 3 - 4 x (- 2 x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

Multiply $5$ by $- 2$ .

$- 10 x^{3} + 5 x^{2} \cdot 3 - 4 x (- 2 x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

Multiply $3$ by $5$ .

$- 10 x^{3} + 15 x^{2} - 4 x (- 2 x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

Rewrite using the commutative property of multiplication.

$- 10 x^{3} + 15 x^{2} - 4 \cdot - 2 x \cdot x - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

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

Move $x$ .

$- 10 x^{3} + 15 x^{2} - 4 \cdot - 2 (x \cdot x) - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

Multiply $x$ by $x$ .

$- 10 x^{3} + 15 x^{2} - 4 \cdot - 2 x^{2} - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

Multiply $- 4$ by $- 2$ .

$- 10 x^{3} + 15 x^{2} + 8 x^{2} - 4 x \cdot 3 + 6 (- 2 x) + 6 \cdot 3$

Multiply $3$ by $- 4$ .

$- 10 x^{3} + 15 x^{2} + 8 x^{2} - 12 x + 6 (- 2 x) + 6 \cdot 3$

Multiply $- 2$ by $6$ .

$- 10 x^{3} + 15 x^{2} + 8 x^{2} - 12 x - 12 x + 6 \cdot 3$

Multiply $6$ by $3$ .

$- 10 x^{3} + 15 x^{2} + 8 x^{2} - 12 x - 12 x + 18$

Simplify by adding terms.

Add $15 x^{2}$ and $8 x^{2}$ .

$- 10 x^{3} + 23 x^{2} - 12 x - 12 x + 18$

Subtract $12 x$ from $- 12 x$ .

$- 10 x^{3} + 23 x^{2} - 24 x + 18$