Question

X2 - x - 6 =

Answer 1

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.

Answer 2

$x^2-x-6=(x+2)(x-3)\\\\-x=2x-3x\\-6=2\times(-3)\\\\or\\\\x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3)$