PLEASE HELP Factoring

i know you add the 1st and 3rd terms
then find 2 numbers that multiply together that get that number.
but those 2 numbers also have to add up to the amount that is the middle term.

but how do i find that number? I need a detailed step by step explanation

example problems:
v^2-4v-60

x^2-13x+36

6x^2+78x+240

k^2+15k+50

a^2-8a+16

I’m going to do the first problem with a fully detailed explanation and just answer the other ones! :)

Factoring: v^2-4v-60

The middle number is -4 and the last number is -60.

Factoring means we want something like

(v+_)(v+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -4

Multiply together to get -60

Can you think of the two numbers?

Try 6 and -10:

6+-10 = -4

6*-10 = -60

Fill in the blanks in

(v+_)(v+_)

with 6 and -10 to get...

(v+6)(v-10)

Second Problem: (x-4)(x-9)

Third Problem: 6(x+5)(x+8)

Fourth Problem: (k+5)(k+10)

Fifth Problem: (a-4)(a-4)