x²-2x-24 = 0

We must factor that. Here's how:

Think of all the ways to write 24 as the product of 2 integers
starting with 24·1:

24·1
12·2
 8·3
 6·4

Since the sign of 24 is -, subtract these out to the side:

24·1   24-1 = 23
12·2   12-2 = 10 
 8·3    8-3 = 5
 6·4    6-4 = 2

Look at the given equation:  x²-2x-24 = 0

The middle term's coefficient (in absolute value) is 2, and
it is listed above in the differences, with 6 and 4.
So we write:

(x 6)(x 4) = 0

and since the middle term is negative, put a - sign with
the larger, 6, and a + sign with the smaller 4

(x-6)(x+4) = 0

Now since the product of (x-6) and (x+4) equals 0, that means
that one of those equals 0.  So we set each  DISABLED_event_one=  0:

x-6 = 0;   x+4 = 0
  x = 6;     x = -4

So there are two solutions, 6 and -4.

We check x = 6 by substituting (6) for x in the original
equation:

    x²-2x-24 = 0
(6)²-2(6)-24 = 0
    36-12-24 = 0
           0 = 0
So x = 6 is a solution:

We check x = -4 by substituting (-4) for x in the original
equation:

      x²-2x-24 = 0
(-4)²-2(-4)-24 = 0
       16+8-24 = 0
             0 = 0
So x = -4 is also a solution:

So we are now certain that x=6 and x=-4 are the solutions
to the given equation.

Edwin