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  a²-8a-180 

The first term is,  a²  its coefficient is  1 .
The middle term is,  -8a  its coefficient is  -8 .
The last term, "the constant", is  -180 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -180 = -180 

Step-2 : Find two factors of  -180  whose sum equals the coefficient of the middle term, which is   -8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  10 
                     a² - 18a + 10a - 180

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (a-18)
              Add up the last 2 terms, pulling out common factors :
                    10 • (a-18)
Step-5 : Add up the four terms of step 4 :
                    (a+10)  •  (a-18)
             Which is the desired factorization

Final result :

  (a + 10) • (a - 18)