Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3m2 +  3m) -  18

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3m² + 3m - 18  =   3 • (m² + m - 6) 

Trying to factor by splitting the middle term

 3.2     Factoring  m² + m - 6 

The first term is,  m²  its coefficient is  1 .
The middle term is,  +m  its coefficient is  1 .
The last term, "the constant", is  -6 

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

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  3 
                     m² - 2m + 3m - 6

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

Final result :

  3 • (m + 3) • (m - 2)