Factor 12x^2-14x-6

$12 x^{2} - 14 x - 6$

Step 1

Factor $2$ out of $12 x^{2} - 14 x - 6$ .

Factor $2$ out of $12 x^{2}$ .

$2 (6 x^{2}) - 14 x - 6$

Factor $2$ out of $- 14 x$ .

$2 (6 x^{2}) + 2 (- 7 x) - 6$

Factor $2$ out of $- 6$ .

$2 (6 x^{2}) + 2 (- 7 x) + 2 (- 3)$

Factor $2$ out of $2 (6 x^{2}) + 2 (- 7 x)$ .

$2 (6 x^{2} - 7 x) + 2 (- 3)$

Factor $2$ out of $2 (6 x^{2} - 7 x) + 2 (- 3)$ .

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

Step 2

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 6 \cdot - 3 = - 18$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

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

Rewrite $- 7$ as $2$ plus $- 9$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

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

Remove unnecessary parentheses.

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

Factor 12x^2-14x-6

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