Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2m2 +  3m) -  9

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2m²+3m-9 

The first term is,  2m²  its coefficient is  2 .
The middle term is,  +3m  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 
                     2m² - 3m + 6m - 9

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

Final result :

  (2m - 3) • (m + 3)