I had a lot of trouble with this when my algebra class started doing it,
a long time ago.
The key is this: Look at the -6 at the end. You have to find two factors
of that number that add up to the -1 in the middle.
Here are the possible factors of -6 :
-1 ... 6
+1 ... -6
-2 ... 3
+2 ... -3
Can you find a pair on the list that adds up to -1 ?
How about +2 and -3 ?
Their product is -6 and their sum is -1. That's what you need.
Now set up a couple of binomial factors like this: (x....) (x....)
and write in the pair of numbers you found: (x + 2) (x - 3)
That's the factored form of the original expression.