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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $2$ .

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

Multiply $- 3$ by $3$ .

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

Multiply $2 x$ by $1$ .

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

Multiply $- 3$ by $1$ .

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

Add $- 9 x$ and $2 x$ .

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