Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (32x2 +  66x) +  21

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   9x² + 66x + 21  =   3 • (3x² + 22x + 7) 

Trying to factor by splitting the middle term

 3.2     Factoring  3x² + 22x + 7 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  +22x  its coefficient is  22 .
The last term, "the constant", is  +7 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 7 = 21 

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   22 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  21 
                     3x² + 1x + 21x + 7

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (3x+1)
              Add up the last 2 terms, pulling out common factors :
                    7 • (3x+1)
Step-5 : Add up the four terms of step 4 :
                    (x+7)  •  (3x+1)
             Which is the desired factorization

Final result :

  3 • (3x + 1) • (x + 7)