Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  n²+4n-12 

The first term is,  n²  its coefficient is  1 .
The middle term is,  +4n  its coefficient is  4 .
The last term, "the constant", is  -12 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -12 = -12 

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   4 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  6 
                     n² - 2n + 6n - 12

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

Final result :

  (n + 6) • (n - 2)