Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  n²-7n-30 

The first term is,  n²  its coefficient is  1 .
The middle term is,  -7n  its coefficient is  -7 .
The last term, "the constant", is  -30 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -30 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  3 
                     n² - 10n + 3n - 30

Step-4 : Add up the first 2 terms, pulling out like factors :
                    n • (n-10)
              Add up the last 2 terms, pulling out common factors :
                    3 • (n-10)
Step-5 : Add up the four terms of step 4 :
                    (n+3)  •  (n-10)
             Which is the desired factorization

Final result :

  (n + 3) • (n - 10)