Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x2 +  11x) +  6

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3x²+11x+6 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  +11x  its coefficient is  11 .
The last term, "the constant", is  +6 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 6 = 18 

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   11 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  9 
                     3x² + 2x + 9x + 6

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (3x+2)
              Add up the last 2 terms, pulling out common factors :
                    3 • (3x+2)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (3x+2)
             Which is the desired factorization

Final result :

  (3x + 2) • (x + 3)