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

$(3 x + 2) (4 x - 5)$

Step 1

Expand $(3 x + 2) (4 x - 5)$ using the FOIL Method.

Apply the distributive property.

$3 x (4 x - 5) + 2 (4 x - 5)$

Apply the distributive property.

$3 x (4 x) + 3 x \cdot - 5 + 2 (4 x - 5)$

Apply the distributive property.

$3 x (4 x) + 3 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 4 x \cdot x + 3 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

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

Move $x$ .

$3 \cdot 4 (x \cdot x) + 3 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

Multiply $x$ by $x$ .

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

Multiply $3$ by $4$ .

$12 x^{2} + 3 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

Multiply $- 5$ by $3$ .

$12 x^{2} - 15 x + 2 (4 x) + 2 \cdot - 5$

Multiply $4$ by $2$ .

$12 x^{2} - 15 x + 8 x + 2 \cdot - 5$

Multiply $2$ by $- 5$ .

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

Add $- 15 x$ and $8 x$ .

$12 x^{2} - 7 x - 10$