Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  a²-20a+99 

The first term is,  a²  its coefficient is  1 .
The middle term is,  -20a  its coefficient is  -20 .
The last term, "the constant", is  +99 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 99 = 99 

Step-2 : Find two factors of  99  whose sum equals the coefficient of the middle term, which is   -20 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -11  and  -9 
                     a² - 11a - 9a - 99

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (a-11)
              Add up the last 2 terms, pulling out common factors :
                    9 • (a-11)
Step-5 : Add up the four terms of step 4 :
                    (a-9)  •  (a-11)
             Which is the desired factorization

Final result :

  (a - 9) • (a - 11)