How do you factor 3a^2-13a-30 ? I know the answer is (3a+5)(a-6)

I know that is the answer, but I don't know how to get there. I was told to factor problems like this:
a^2+2a+1

I first multiply the outside numbers together, which equals 1. I then find the factors of 1 that will equal the middle number (2), which are 1and 1. So, the answer for this problem would be (a+1)(a+1).

This problem is different, though. When I multiple 3 and 30 together I get 90 and there's no factors of 90 to equal -13 as -13 is a prime number. What do I do here?

The general form of a trinomial is Ax² + Bx + C. When A is not equal to 1, this is what I do:
Multiply AC = 3(30) = 90. Since the second sign is negative, the two signs in parentheses have to be opposites. (+)(–).
Factor 90 into its components to find two numbers that will subtract to 13
90 = 9 * 10 = 3 * 3 * 2 * 5. Mix and match until you find the right combination: 18*5 = 90 and 18–5=13
Here's a little hook:
Put 3a into both parentheses:
(3a + )(3a – )
Since we need to get a negative 13, put the 18 behind the negative sign:
(3a + 5)(3a – 18)
If this method is to work, at least one of the parentheses has to have a reducible form. Note that the second term reduces by 3.
(3a + 5)(a – 6)

to factor 3a^2-13a-30
3(--30) = -- 90 = (--18)(5) where -- 18 + 5 = -- 13, the middle coefficient
then
3a^2-13a-30 = 3a^2 -- 18a + 5a -- 30 = 3a(a -- 6) + 5(a -- 6) = (a -- 6)(3a + 5)

3a^2-13a-30
3a^2 - 18a + 5a - 30
3a(a - 6) + 5(a - 6)
(3a + 5) (a - 6)