Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "p2"   was replaced by   "p^2". 

Step  1  :

Equation at the end of step  1  :

  (25p2 -  60p) -  27

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  32p²-60p-27 

The first term is,  32p²  its coefficient is  32 .
The middle term is,  -60p  its coefficient is  -60 .
The last term, "the constant", is  -27 

Step-1 : Multiply the coefficient of the first term by the constant   32 • -27 = -864 

Step-2 : Find two factors of  -864  whose sum equals the coefficient of the middle term, which is   -60 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -72  and  12 
                     32p² - 72p + 12p - 27

Step-4 : Add up the first 2 terms, pulling out like factors :
                    8p • (4p-9)
              Add up the last 2 terms, pulling out common factors :
                    3 • (4p-9)
Step-5 : Add up the four terms of step 4 :
                    (8p+3)  •  (4p-9)
             Which is the desired factorization

Final result :

  (4p - 9) • (8p + 3)