Question

how do you factor the second equation?

Answer 1

the answer is (2x+1)(x-5)

Answer 2

Ax^2+Bx+C=0
if A and C have different signs, then so are the two factors.

2x^2-9x-5=0
Here 2 and -5 have different signs.

So try
(2x+M)(X+N) such that MN=-5, M+2N=-9
Try M=1 N=-5  MN=-5, M+2N=-9
so
(2x+1)(x-5)=0