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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $3$ .

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

Multiply $- 5$ by $2$ .

$6 x^{2} - 10 x + 3 (3 x) + 3 \cdot - 5$

Multiply $3$ by $3$ .

$6 x^{2} - 10 x + 9 x + 3 \cdot - 5$

Multiply $3$ by $- 5$ .

$6 x^{2} - 10 x + 9 x - 15$

Add $- 10 x$ and $9 x$ .

$6 x^{2} - x - 15$