Write this:

(x    )(x     )

Look at the 72 of " x² + 6x - 72 "

It is negative, so think "SUBTRACT". 
(If it had been positive you would think "ADD")

Look at the 6 of " x² + 6x - 72 ".

Think of two whole numbers that when multiplied 
give 72 and, when SUBTRACTED, give 6?

Go thru pairs of integers which multiply to give 
72, and see if when you SUBTRACT them, larger
minus smaller, you get 6.

72 = 1x72, but 72-1 = 70, not 6
72 = 2x36, but 36-2 = 34, not 6
72 = 3x24, but 24-3 = 21, not 6
72 = 4x18, but 18-4 = 14, not 6
72 = 6x12, and 12-6 = 6.  Hey that's it!

Now write just the 6 and the 12 at the 
right ends of those two parentheses:

So you have this now:

(x   6)(x   12) 

Now look at the sign before the middle 
term of " x² + 6x - 72 ". It is plus, 
so put a plus next to the larger number, 
which is 12.  So now you have

(x   6)(x + 12)

Now you only need to find what sign to 
put in the first parentheses.

Since the last term of " x² + 6x - 72 " 
is negative, put the OPPOSITE sign before 
the 6 that you put before the 12.  Since
you oput a plus sign before the 12, you 
will put a minus sign before the 6. 

(x - 6)(x + 12)

(If it were positive, you would have put 
the SAME sign instead.)

Edwin