Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3•7n2) -  81n) +  15

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   84n² - 81n + 15  =   3 • (28n² - 27n + 5) 

Trying to factor by splitting the middle term

 3.2     Factoring  28n² - 27n + 5 

The first term is,  28n²  its coefficient is  28 .
The middle term is,  -27n  its coefficient is  -27 .
The last term, "the constant", is  +5 

Step-1 : Multiply the coefficient of the first term by the constant   28 • 5 = 140 

Step-2 : Find two factors of  140  whose sum equals the coefficient of the middle term, which is   -27 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  -7 
                     28n² - 20n - 7n - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
                    4n • (7n-5)
              Add up the last 2 terms, pulling out common factors :
                     1 • (7n-5)
Step-5 : Add up the four terms of step 4 :
                    (4n-1)  •  (7n-5)
             Which is the desired factorization

Final result :

  3 • (7n - 5) • (4n - 1)