Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  g²-3g-180 

The first term is,  g²  its coefficient is  1 .
The middle term is,  -3g  its coefficient is  -3 .
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   -3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  12 
                     g² - 15g + 12g - 180

Step-4 : Add up the first 2 terms, pulling out like factors :
                    g • (g-15)
              Add up the last 2 terms, pulling out common factors :
                    12 • (g-15)
Step-5 : Add up the four terms of step 4 :
                    (g+12)  •  (g-15)
             Which is the desired factorization

Final result :

  (g + 12) • (g - 15)