Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2p2 -  2p) -  12

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2p² - 2p - 12  =   2 • (p² - p - 6) 

Trying to factor by splitting the middle term

 3.2     Factoring  p² - p - 6 

The first term is,  p²  its coefficient is  1 .
The middle term is,  -p  its coefficient is  -1 .
The last term, "the constant", is  -6 

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

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -1 .

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

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

Final result :

  2 • (p + 2) • (p - 3)