Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2n2 +  3n) -  9

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2n²+3n-9 

The first term is,  2n²  its coefficient is  2 .
The middle term is,  +3n  its coefficient is  3 .
The last term, "the constant", is  -9 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -9 = -18 

Step-2 : Find two factors of  -18  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,  -3  and  6 
                     2n² - 3n + 6n - 9

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

Final result :

  (2n - 3) • (n + 3)