Factor 6a2 - 8a - 30 completely

6a^2 - 8a - 30

= 2 (3a^2 - 4a - 15)

= 2 (3a^2 - 9a + 5a - 15)

= 2 {3a (a-3) + 5 (a-3) }

= 2 (3a+5) (a-3)

First separate out the common scalar factor 2 to get: 6a2-8a-30=2 (3a2-4a-15)

Next find a pair of factors of 3*15=45 which differ by 4. The pair 9, 5 works.

Then you find:

3 a2 - 4a-15 = 3 a2 - 9a+5a-15 = (3 a2 - 9a) + (5a-15) = 3a (a-3) + 5 (a-3) = (3a+5) (a-3)

Putting this all together:

6 a2 - 8a-30=2 (3 a2 - 4a-15) = 2 (3a+5) (a-3)