Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (24m2 +  60m) -  54

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   16m² + 60m - 54  =   2 • (8m² + 30m - 27) 

Trying to factor by splitting the middle term

 3.2     Factoring  8m² + 30m - 27 

The first term is,  8m²  its coefficient is  8 .
The middle term is,  +30m  its coefficient is  30 .
The last term, "the constant", is  -27 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -27 = -216 

Step-2 : Find two factors of  -216  whose sum equals the coefficient of the middle term, which is   30 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  36 
                     8m² - 6m + 36m - 27

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2m • (4m-3)
              Add up the last 2 terms, pulling out common factors :
                    9 • (4m-3)
Step-5 : Add up the four terms of step 4 :
                    (2m+9)  •  (4m-3)
             Which is the desired factorization

Final result :

  2 • (4m - 3) • (2m + 9)