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".  3 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

   ((2•(p2))-6p) ((2p2-p)-21)
  (—————————————•————————————)•p2
   (7p-(2•(p2)))      9      

Step  2  :

            2p2 - p - 21
 Simplify   ————————————
                 9      

Trying to factor by splitting the middle term

 2.1     Factoring  2p² - p - 21 

The first term is,  2p²  its coefficient is  2 .
The middle term is,  -p  its coefficient is  -1 .
The last term, "the constant", is  -21 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -21 = -42 

Step-2 : Find two factors of  -42  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,  -7  and  6 
                     2p² - 7p + 6p - 21

Step-4 : Add up the first 2 terms, pulling out like factors :
                    p • (2p-7)
              Add up the last 2 terms, pulling out common factors :
                    3 • (2p-7)
Step-5 : Add up the four terms of step 4 :
                    (p+3)  •  (2p-7)
             Which is the desired factorization

Equation at the end of step  2  :

   ((2•(p2))-6p) (2p-7)•(p+3)
  (—————————————•————————————)•p2
   (7p-(2•(p2)))      9      
 Step  3  :

Equation at the end of step  3  :

   ((2•(p2))-6p) (2p-7)•(p+3)
  (—————————————•————————————)•p2
     (7p-2p2)         9      
 Step  4  :

Equation at the end of step  4  :

   (2p2-6p) (2p-7)•(p+3)
  (————————•————————————)•p2
   (7p-2p2)      9      

Step  5  :

            2p2 - 6p
 Simplify   ————————
            7p - 2p2

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   2p² - 6p  =   2p • (p - 3) 

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   7p - 2p²  =   -p • (2p - 7) 

Canceling Out :

 7.2    Canceling out p as it appears on both sides of the fraction line  7.3      Attempting Polynomial Long Division

   Attempted Long division of
      p - 3 
   By :
      7 - 2p 
   Was aborted due to the followinf reason :

   Dividend and Divisor do not share same variable

Equation at the end of step  7  :

   2 • (p - 3)   (2p - 7) • (p + 3)
  (——————————— • ——————————————————) • p2
     7 - 2p              9         

Step  8  :

 8.1    Rewrite   (7-2p)    as  (-1) •  (2p-7) 

Canceling Out :

 8.2    Cancel out  (2p-7)  which now appears on both sides of the fraction line.

Equation at the end of step  8  :

  -2 • (p - 3) • (p + 3)
  —————————————————————— • p2
            9           

Step  9  :

Final result :

  -2p2 • (p - 3) • (p + 3)
  ————————————————————————
             9