Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3p2 -  2p) -  5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3p²-2p-5 

The first term is,  3p²  its coefficient is  3 .
The middle term is,  -2p  its coefficient is  -2 .
The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -5 = -15 

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is   -2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  3 
                     3p² - 5p + 3p - 5

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

Final result :

  (3p - 5) • (p + 1)