Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x2 +  42x) +  39

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3x² + 42x + 39  =   3 • (x² + 14x + 13) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² + 14x + 13 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +14x  its coefficient is  14 .
The last term, "the constant", is  +13 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 13 = 13 

Step-2 : Find two factors of  13  whose sum equals the coefficient of the middle term, which is   14 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  13 
                     x² + 1x + 13x + 13

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x+1)
              Add up the last 2 terms, pulling out common factors :
                    13 • (x+1)
Step-5 : Add up the four terms of step 4 :
                    (x+13)  •  (x+1)
             Which is the desired factorization

Final result :

  3 • (x + 13) • (x + 1)