Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3r2 +  9r) +  6

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3r² + 9r + 6  =   3 • (r² + 3r + 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  r² + 3r + 2 

The first term is,  r²  its coefficient is  1 .
The middle term is,  +3r  its coefficient is  3 .
The last term, "the constant", is  +2 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 2 = 2 

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  2 
                     r² + 1r + 2r + 2

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

Final result :

  3 • (r + 2) • (r + 1)