Simplify (3x+5)(2x-7)

$(3 x + 5) (2 x - 7)$

Step 1

Expand $(3 x + 5) (2 x - 7)$ using the FOIL Method.

Apply the distributive property.

$3 x (2 x - 7) + 5 (2 x - 7)$

Apply the distributive property.

$3 x (2 x) + 3 x \cdot - 7 + 5 (2 x - 7)$

Apply the distributive property.

$3 x (2 x) + 3 x \cdot - 7 + 5 (2 x) + 5 \cdot - 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x + 3 x \cdot - 7 + 5 (2 x) + 5 \cdot - 7$

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

Move $x$ .

$3 \cdot 2 (x \cdot x) + 3 x \cdot - 7 + 5 (2 x) + 5 \cdot - 7$

Multiply $x$ by $x$ .

$3 \cdot 2 x^{2} + 3 x \cdot - 7 + 5 (2 x) + 5 \cdot - 7$

Multiply $3$ by $2$ .

$6 x^{2} + 3 x \cdot - 7 + 5 (2 x) + 5 \cdot - 7$

Multiply $- 7$ by $3$ .

$6 x^{2} - 21 x + 5 (2 x) + 5 \cdot - 7$

Multiply $2$ by $5$ .

$6 x^{2} - 21 x + 10 x + 5 \cdot - 7$

Multiply $5$ by $- 7$ .

$6 x^{2} - 21 x + 10 x - 35$

Add $- 21 x$ and $10 x$ .

$6 x^{2} - 11 x - 35$