Factor 24d^2+39d-18

$24 d^{2} + 39 d - 18$

Step 1

Factor $3$ out of $24 d^{2} + 39 d - 18$ .

Factor $3$ out of $24 d^{2}$ .

$3 (8 d^{2}) + 39 d - 18$

Factor $3$ out of $39 d$ .

$3 (8 d^{2}) + 3 (13 d) - 18$

Factor $3$ out of $- 18$ .

$3 (8 d^{2}) + 3 (13 d) + 3 (- 6)$

Factor $3$ out of $3 (8 d^{2}) + 3 (13 d)$ .

$3 (8 d^{2} + 13 d) + 3 (- 6)$

Factor $3$ out of $3 (8 d^{2} + 13 d) + 3 (- 6)$ .

$3 (8 d^{2} + 13 d - 6)$

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 $a \cdot c = 8 \cdot - 6 = - 48$ and whose sum is $b = 13$ .

Factor $13$ out of $13 d$ .

$3 (8 d^{2} + 13 (d) - 6)$

Rewrite $13$ as $- 3$ plus $16$

$3 (8 d^{2} + (- 3 + 16) d - 6)$

Apply the distributive property.

$3 (8 d^{2} - 3 d + 16 d - 6)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((8 d^{2} - 3 d) + 16 d - 6)$

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

$3 (d (8 d - 3) + 2 (8 d - 3))$

Factor the polynomial by factoring out the greatest common factor, $8 d - 3$ .

$3 ((8 d - 3) (d + 2))$

Remove unnecessary parentheses.

$3 (8 d - 3) (d + 2)$

Factor 24d^2+39d-18

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