Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  d²-5d-66 

The first term is,  d²  its coefficient is  1 .
The middle term is,  -5d  its coefficient is  -5 .
The last term, "the constant", is  -66 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -66 = -66 

Step-2 : Find two factors of  -66  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,  -11  and  6 
                     d² - 11d + 6d - 66

Step-4 : Add up the first 2 terms, pulling out like factors :
                    d • (d-11)
              Add up the last 2 terms, pulling out common factors :
                    6 • (d-11)
Step-5 : Add up the four terms of step 4 :
                    (d+6)  •  (d-11)
             Which is the desired factorization

Final result :

  (d + 6) • (d - 11)