Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2r2 +  3r) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2r²+3r+1 

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

Step-1 : Multiply the coefficient of the first term by the constant   2 • 1 = 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 
                     2r² + 1r + 2r + 1

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

Final result :

  (2r + 1) • (r + 1)