6x²-13x+6
 

Multiply the 6 by the 6 ignoring signs.  Get 36

Write down all the ways to have two positive integers
which have product 36, starting with 36*1

36*1
18*2
12*3
 9*4
 6*6

Since the last sign 6x²-13x+6 is +, ADD them,
and place the SUM out beside that:

36*1   36+1=37
18*2   18+2=20 
12*3   12+3=15
 9*4    9+4=13
 6*6    6+6=12

Now, again ignoring signs, we find in that list of
sums the coefficient of the middle term in 6x²-13x+6


So we replace the number 13 by 9+4

6x²-13x+6
6x²-(9+4)x+6

Then we distribute to remove the parentheses:

6x²-9x-4x+6

Factor the first two terms 6x²-9x by taking out the
greatest common factor, 3x, getting 3x(2x-3)

Factor the last two terms -4x+6 by taking out the
greatest common factor, getting -2(2x-3)

So we have

3x(2x-3)-2(2x-3)

Notice that there is a common factor, (2x-3)

3x(2x-3)-2(2x-3)

which we can factor out leaving the 3x and the -2 to put 
in parentheses:

(2x-3)(3x-2)

Edwin