Factor 15n^2-27n-6

$15 n^{2} - 27 n - 6$

Step 1

Factor $3$ out of $15 n^{2} - 27 n - 6$ .

Factor $3$ out of $15 n^{2}$ .

$3 (5 n^{2}) - 27 n - 6$

Factor $3$ out of $- 27 n$ .

$3 (5 n^{2}) + 3 (- 9 n) - 6$

Factor $3$ out of $- 6$ .

$3 (5 n^{2}) + 3 (- 9 n) + 3 (- 2)$

Factor $3$ out of $3 (5 n^{2}) + 3 (- 9 n)$ .

$3 (5 n^{2} - 9 n) + 3 (- 2)$

Factor $3$ out of $3 (5 n^{2} - 9 n) + 3 (- 2)$ .

$3 (5 n^{2} - 9 n - 2)$

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 $a \cdot c = 5 \cdot - 2 = - 10$ and whose sum is $b = - 9$ .

Factor $- 9$ out of $- 9 n$ .

$3 (5 n^{2} - 9 (n) - 2)$

Rewrite $- 9$ as $1$ plus $- 10$

$3 (5 n^{2} + (1 - 10) n - 2)$

Apply the distributive property.

$3 (5 n^{2} + 1 n - 10 n - 2)$

Multiply $n$ by $1$ .

$3 (5 n^{2} + n - 10 n - 2)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((5 n^{2} + n) - 10 n - 2)$

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

$3 (n (5 n + 1) - 2 (5 n + 1))$

Factor the polynomial by factoring out the greatest common factor, $5 n + 1$ .

$3 ((5 n + 1) (n - 2))$

Remove unnecessary parentheses.

$3 (5 n + 1) (n - 2)$

Factor 15n^2-27n-6

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