Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3p2 -  7p) -  40

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3p²-7p-40 

The first term is,  3p²  its coefficient is  3 .
The middle term is,  -7p  its coefficient is  -7 .
The last term, "the constant", is  -40 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -40 = -120 

Step-2 : Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  8 
                     3p² - 15p + 8p - 40

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3p • (p-5)
              Add up the last 2 terms, pulling out common factors :
                    8 • (p-5)
Step-5 : Add up the four terms of step 4 :
                    (3p+8)  •  (p-5)
             Which is the desired factorization

Final result :

  (p - 5) • (3p + 8)