Hi, I really need some help understanding this question. I've watched multiple videos online but it seems for this question its complete opposite.

Factoring by Trinomial:

6x27x5

Step1: 6x * 5 = -30 , 3-10= -7, 3*-10=30

Step2:6x2+3x10x5

step3: GCF 6 & 3 = 3 10 & 5 = 5

step4: 3x(3x+1) -5(2x+1)

step5: (3x+1)(3x-5) -- After watching multiple videos this just seems like the correct way. The answer is (3x-5)(2x+1)

I just cant seem to understand why -5 goes to the first set instead of the second?

Any help would be greatly appreciated. Thanks.