Simplify (4x+1)(3x-4)-(5x^2-10x-12)

$(4 x + 1) (3 x - 4) - (5 x^{2} - 10 x - 12)$

Step 1

Simplify each term.

Expand $(4 x + 1) (3 x - 4)$ using the FOIL Method.

Apply the distributive property.

$4 x (3 x - 4) + 1 (3 x - 4) - (5 x^{2} - 10 x - 12)$

Apply the distributive property.

$4 x (3 x) + 4 x \cdot - 4 + 1 (3 x - 4) - (5 x^{2} - 10 x - 12)$

Apply the distributive property.

$4 x (3 x) + 4 x \cdot - 4 + 1 (3 x) + 1 \cdot - 4 - (5 x^{2} - 10 x - 12)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 3 x \cdot x + 4 x \cdot - 4 + 1 (3 x) + 1 \cdot - 4 - (5 x^{2} - 10 x - 12)$

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

Move $x$ .

$4 \cdot 3 (x \cdot x) + 4 x \cdot - 4 + 1 (3 x) + 1 \cdot - 4 - (5 x^{2} - 10 x - 12)$

Multiply $x$ by $x$ .

$4 \cdot 3 x^{2} + 4 x \cdot - 4 + 1 (3 x) + 1 \cdot - 4 - (5 x^{2} - 10 x - 12)$

Multiply $4$ by $3$ .

$12 x^{2} + 4 x \cdot - 4 + 1 (3 x) + 1 \cdot - 4 - (5 x^{2} - 10 x - 12)$

Multiply $- 4$ by $4$ .

$12 x^{2} - 16 x + 1 (3 x) + 1 \cdot - 4 - (5 x^{2} - 10 x - 12)$

Multiply $3 x$ by $1$ .

$12 x^{2} - 16 x + 3 x + 1 \cdot - 4 - (5 x^{2} - 10 x - 12)$

Multiply $- 4$ by $1$ .

$12 x^{2} - 16 x + 3 x - 4 - (5 x^{2} - 10 x - 12)$

Add $- 16 x$ and $3 x$ .

$12 x^{2} - 13 x - 4 - (5 x^{2} - 10 x - 12)$

Apply the distributive property.

$12 x^{2} - 13 x - 4 - (5 x^{2}) - (- 10 x) - - 12$

Simplify.

Multiply $5$ by $- 1$ .

$12 x^{2} - 13 x - 4 - 5 x^{2} - (- 10 x) - - 12$

Multiply $- 10$ by $- 1$ .

$12 x^{2} - 13 x - 4 - 5 x^{2} + 10 x - - 12$

Multiply $- 1$ by $- 12$ .

$12 x^{2} - 13 x - 4 - 5 x^{2} + 10 x + 12$

Step 2

Simplify by adding terms.

Subtract $5 x^{2}$ from $12 x^{2}$ .

$7 x^{2} - 13 x - 4 + 10 x + 12$

Add $- 13 x$ and $10 x$ .

$7 x^{2} - 3 x - 4 + 12$

Add $- 4$ and $12$ .

$7 x^{2} - 3 x + 8$

Simplify (4x+1)(3x-4)-(5x^2-10x-12)

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