Simplify (2x-3)(3x+1)

$(2 x - 3) (3 x + 1)$

Step 1

Expand $(2 x - 3) (3 x + 1)$ using the FOIL Method.

Apply the distributive property.

$2 x (3 x + 1) - 3 (3 x + 1)$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot 1 - 3 (3 x + 1)$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot 1 - 3 (3 x) - 3 \cdot 1$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x \cdot 1 - 3 (3 x) - 3 \cdot 1$

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

Move $x$ .

$2 \cdot 3 (x \cdot x) + 2 x \cdot 1 - 3 (3 x) - 3 \cdot 1$

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} + 2 x \cdot 1 - 3 (3 x) - 3 \cdot 1$

Multiply $2$ by $3$ .

$6 x^{2} + 2 x \cdot 1 - 3 (3 x) - 3 \cdot 1$

Multiply $2$ by $1$ .

$6 x^{2} + 2 x - 3 (3 x) - 3 \cdot 1$

Multiply $3$ by $- 3$ .

$6 x^{2} + 2 x - 9 x - 3 \cdot 1$

Multiply $- 3$ by $1$ .

$6 x^{2} + 2 x - 9 x - 3$

Subtract $9 x$ from $2 x$ .

$6 x^{2} - 7 x - 3$