Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²+9x+14 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +9x  its coefficient is  9 .
The last term, "the constant", is  +14 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 14 = 14 

Step-2 : Find two factors of  14  whose sum equals the coefficient of the middle term, which is   9 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  7 
                     x² + 2x + 7x + 14

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x+2)
              Add up the last 2 terms, pulling out common factors :
                    7 • (x+2)
Step-5 : Add up the four terms of step 4 :
                    (x+7)  •  (x+2)
             Which is the desired factorization

Final result :

  (x + 7) • (x + 2)