Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3m2 +  10m) +  3

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3m²+10m+3 

The first term is,  3m²  its coefficient is  3 .
The middle term is,  +10m  its coefficient is  10 .
The last term, "the constant", is  +3 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 3 = 9 

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   10 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  9 
                     3m² + 1m + 9m + 3

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

Final result :

  (3m + 1) • (m + 3)