We know the factorization will result in two binomials, so let's just write the parentheses for it:
( )( )
Since the coefficient of the first term is 1, we know that the first two terms of the binomial will simply be
(X )(X )
Now, the second terms of the binomial are found from finding two factors that multiply to give the last term, but also sum to give the middle term. You can just list the factors, always looking for a combination that is suspected of adding to give the middle term given some combination of signs. Knowing divisibility rules can help make this a little faster.
x2 + 99x - 3870 = 0
We're looking for factors of 3870 that add together to give the middle term:
30 and 129 look good. What would their signs have to be in order to sum to 99? ( -30 and +129)
So these are the other two factors.
(X - 30)(X + 129) ==> you can always FOIL this to make sure you have the right factorization.