Simplify (3x^2-11x-4)-(x-2)(2x+3)

$(3 x^{2} - 11 x - 4) - (x - 2) (2 x + 3)$

Simplify each term.

Apply the distributive property.

$3 x^{2} - 11 x - 4 + (- x - - 2) (2 x + 3)$

Multiply $- 1$ by $- 2$ .

$3 x^{2} - 11 x - 4 + (- x + 2) (2 x + 3)$

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

Apply the distributive property.

$3 x^{2} - 11 x - 4 - x (2 x + 3) + 2 (2 x + 3)$

Apply the distributive property.

$3 x^{2} - 11 x - 4 - x (2 x) - x \cdot 3 + 2 (2 x + 3)$

Apply the distributive property.

$3 x^{2} - 11 x - 4 - x (2 x) - x \cdot 3 + 2 (2 x) + 2 \cdot 3$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 x^{2} - 11 x - 4 - 1 \cdot 2 x \cdot x - x \cdot 3 + 2 (2 x) + 2 \cdot 3$

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

Move $x$ .

$3 x^{2} - 11 x - 4 - 1 \cdot 2 (x \cdot x) - x \cdot 3 + 2 (2 x) + 2 \cdot 3$

Multiply $x$ by $x$ .

$3 x^{2} - 11 x - 4 - 1 \cdot 2 x^{2} - x \cdot 3 + 2 (2 x) + 2 \cdot 3$

Multiply $- 1$ by $2$ .

$3 x^{2} - 11 x - 4 - 2 x^{2} - x \cdot 3 + 2 (2 x) + 2 \cdot 3$

Multiply $3$ by $- 1$ .

$3 x^{2} - 11 x - 4 - 2 x^{2} - 3 x + 2 (2 x) + 2 \cdot 3$

Multiply $2$ by $2$ .

$3 x^{2} - 11 x - 4 - 2 x^{2} - 3 x + 4 x + 2 \cdot 3$

Multiply $2$ by $3$ .

$3 x^{2} - 11 x - 4 - 2 x^{2} - 3 x + 4 x + 6$

Add $- 3 x$ and $4 x$ .

$3 x^{2} - 11 x - 4 - 2 x^{2} + x + 6$

Simplify by adding terms.

Subtract $2 x^{2}$ from $3 x^{2}$ .

$x^{2} - 11 x - 4 + x + 6$

Add $- 11 x$ and $x$ .

$x^{2} - 10 x - 4 + 6$

Add $- 4$ and $6$ .

$x^{2} - 10 x + 2$