Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²+19x+78 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +19x  its coefficient is  19 .
The last term, "the constant", is  +78 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 78 = 78 

Step-2 : Find two factors of  78  whose sum equals the coefficient of the middle term, which is   19 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  6  and  13 
                     x² + 6x + 13x + 78

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x+6)
              Add up the last 2 terms, pulling out common factors :
                    13 • (x+6)
Step-5 : Add up the four terms of step 4 :
                    (x+13)  •  (x+6)
             Which is the desired factorization

Final result :

  (x + 13) • (x + 6)