Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3x2) -  13x) +  6

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  6x²-13x+6 

The first term is,  6x²  its coefficient is  6 .
The middle term is,  -13x  its coefficient is  -13 .
The last term, "the constant", is  +6 

Step-1 : Multiply the coefficient of the first term by the constant   6 • 6 = 36 

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -4 
                     6x² - 9x - 4x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3x • (2x-3)
              Add up the last 2 terms, pulling out common factors :
                    2 • (2x-3)
Step-5 : Add up the four terms of step 4 :
                    (3x-2)  •  (2x-3)
             Which is the desired factorization

Final result :

  (2x - 3) • (3x - 2)