Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3n2 +  8n) +  4

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3n²+8n+4 

The first term is,  3n²  its coefficient is  3 .
The middle term is,  +8n  its coefficient is  8 .
The last term, "the constant", is  +4 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 4 = 12 

Step-2 : Find two factors of  12  whose sum equals the coefficient of the middle term, which is   8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  6 
                     3n² + 2n + 6n + 4

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

Final result :

  (3n + 2) • (n + 2)