Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3n2 +  5n) -  2

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3n²+5n-2 

The first term is,  3n²  its coefficient is  3 .
The middle term is,  +5n  its coefficient is  5 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -2 = -6 

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  6 
                     3n² - 1n + 6n - 2

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

Final result :

  (3n - 1) • (n + 2)