2a^2 - 21a - 65
We should end up with something like (?a + ?)(?a + ?)
The only way to make 2 (out of whole numbers) is 2 * 1, so we should have (2a + ?)(a + ?)
We can make 65 with 1 * 65 and 5 * 13. Let's try 5 * 13. Notice that 5*1 - 13*2 = -21, which we want for the a.
(2a + ?)(a + ?)
(2a + 5)(a - 13)
Check it with FOIL:
2a^2 + 2a(-13) + 5(a) + 5(-13)
2a^2 - 26a + 5a - 65
2a^2 - 21a - 65
It matches the original problem, so it works.
Answer: (2a+5)(a-13)