Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "a2"   was replaced by   "a^2". 

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  a²-5a-6 

The first term is,  a²  its coefficient is  1 .
The middle term is,  -5a  its coefficient is  -5 .
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   -5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  1 
                     a² - 6a + 1a - 6

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (a-6)
              Add up the last 2 terms, pulling out common factors :
                     1 • (a-6)
Step-5 : Add up the four terms of step 4 :
                    (a+1)  •  (a-6)
             Which is the desired factorization

Final result :

  (a + 1) • (a - 6)