Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3p2) -  11p) +  3

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  6p²-11p+3 

The first term is,  6p²  its coefficient is  6 .
The middle term is,  -11p  its coefficient is  -11 .
The last term, "the constant", is  +3 

Step-1 : Multiply the coefficient of the first term by the constant   6 • 3 = 18 

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   -11 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -2 
                     6p² - 9p - 2p - 3

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3p • (2p-3)
              Add up the last 2 terms, pulling out common factors :
                     1 • (2p-3)
Step-5 : Add up the four terms of step 4 :
                    (3p-1)  •  (2p-3)
             Which is the desired factorization

Final result :

  (2p - 3) • (3p - 1)