Simplify (2x+7)(3x-4)

$(2 x + 7) (3 x - 4)$

Step 1

Expand $(2 x + 7) (3 x - 4)$ using the FOIL Method.

Apply the distributive property.

$2 x (3 x - 4) + 7 (3 x - 4)$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot - 4 + 7 (3 x - 4)$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot - 4 + 7 (3 x) + 7 \cdot - 4$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x \cdot - 4 + 7 (3 x) + 7 \cdot - 4$

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

Move $x$ .

$2 \cdot 3 (x \cdot x) + 2 x \cdot - 4 + 7 (3 x) + 7 \cdot - 4$

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} + 2 x \cdot - 4 + 7 (3 x) + 7 \cdot - 4$

Multiply $2$ by $3$ .

$6 x^{2} + 2 x \cdot - 4 + 7 (3 x) + 7 \cdot - 4$

Multiply $- 4$ by $2$ .

$6 x^{2} - 8 x + 7 (3 x) + 7 \cdot - 4$

Multiply $3$ by $7$ .

$6 x^{2} - 8 x + 21 x + 7 \cdot - 4$

Multiply $7$ by $- 4$ .

$6 x^{2} - 8 x + 21 x - 28$

Add $- 8 x$ and $21 x$ .

$6 x^{2} + 13 x - 28$