Factor 20x^2-54x+36

$20 x^{2} - 54 x + 36$

Step 1

Factor $2$ out of $20 x^{2} - 54 x + 36$ .

Factor $2$ out of $20 x^{2}$ .

$2 (10 x^{2}) - 54 x + 36$

Factor $2$ out of $- 54 x$ .

$2 (10 x^{2}) + 2 (- 27 x) + 36$

Factor $2$ out of $36$ .

$2 (10 x^{2}) + 2 (- 27 x) + 2 (18)$

Factor $2$ out of $2 (10 x^{2}) + 2 (- 27 x)$ .

$2 (10 x^{2} - 27 x) + 2 (18)$

Factor $2$ out of $2 (10 x^{2} - 27 x) + 2 (18)$ .

$2 (10 x^{2} - 27 x + 18)$

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 $a \cdot c = 10 \cdot 18 = 180$ and whose sum is $b = - 27$ .

Factor $- 27$ out of $- 27 x$ .

$2 (10 x^{2} - 27 (x) + 18)$

Rewrite $- 27$ as $- 12$ plus $- 15$

$2 (10 x^{2} + (- 12 - 15) x + 18)$

Apply the distributive property.

$2 (10 x^{2} - 12 x - 15 x + 18)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((10 x^{2} - 12 x) - 15 x + 18)$

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

$2 (2 x (5 x - 6) - 3 (5 x - 6))$

Factor the polynomial by factoring out the greatest common factor, $5 x - 6$ .

$2 ((5 x - 6) (2 x - 3))$

Remove unnecessary parentheses.

$2 (5 x - 6) (2 x - 3)$

Factor 20x^2-54x+36

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