Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2n2 -  9n) -  11

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2n²-9n-11 

The first term is,  2n²  its coefficient is  2 .
The middle term is,  -9n  its coefficient is  -9 .
The last term, "the constant", is  -11 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -11 = -22 

Step-2 : Find two factors of  -22  whose sum equals the coefficient of the middle term, which is   -9 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -11  and  2 
                     2n² - 11n + 2n - 11

Step-4 : Add up the first 2 terms, pulling out like factors :
                    n • (2n-11)
              Add up the last 2 terms, pulling out common factors :
                     1 • (2n-11)
Step-5 : Add up the four terms of step 4 :
                    (n+1)  •  (2n-11)
             Which is the desired factorization

Final result :

  (2n - 11) • (n + 1)