Simplify (3x+4)(2x-6)

$(3 x + 4) (2 x - 6)$

Step 1

Expand $(3 x + 4) (2 x - 6)$ using the FOIL Method.

Apply the distributive property.

$3 x (2 x - 6) + 4 (2 x - 6)$

Apply the distributive property.

$3 x (2 x) + 3 x \cdot - 6 + 4 (2 x - 6)$

Apply the distributive property.

$3 x (2 x) + 3 x \cdot - 6 + 4 (2 x) + 4 \cdot - 6$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x + 3 x \cdot - 6 + 4 (2 x) + 4 \cdot - 6$

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

Move $x$ .

$3 \cdot 2 (x \cdot x) + 3 x \cdot - 6 + 4 (2 x) + 4 \cdot - 6$

Multiply $x$ by $x$ .

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

Multiply $3$ by $2$ .

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

Multiply $- 6$ by $3$ .

$6 x^{2} - 18 x + 4 (2 x) + 4 \cdot - 6$

Multiply $2$ by $4$ .

$6 x^{2} - 18 x + 8 x + 4 \cdot - 6$

Multiply $4$ by $- 6$ .

$6 x^{2} - 18 x + 8 x - 24$

Add $- 18 x$ and $8 x$ .

$6 x^{2} - 10 x - 24$