Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3p2 -  14p) +  8

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3p²-14p+8 

The first term is,  3p²  its coefficient is  3 .
The middle term is,  -14p  its coefficient is  -14 .
The last term, "the constant", is  +8 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 8 = 24 

Step-2 : Find two factors of  24  whose sum equals the coefficient of the middle term, which is   -14 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  -2 
                     3p² - 12p - 2p - 8

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

Final result :

  (p - 4) • (3p - 2)