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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $4$ .

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

Multiply $- 3$ by $3$ .

$12 x^{2} - 9 x + 2 (4 x) + 2 \cdot - 3$

Multiply $4$ by $2$ .

$12 x^{2} - 9 x + 8 x + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$12 x^{2} - 9 x + 8 x - 6$

Add $- 9 x$ and $8 x$ .

$12 x^{2} - x - 6$