Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•32m2) -  21m) -  30

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   36m² - 21m - 30  =   3 • (12m² - 7m - 10) 

Trying to factor by splitting the middle term

 3.2     Factoring  12m² - 7m - 10 

The first term is,  12m²  its coefficient is  12 .
The middle term is,  -7m  its coefficient is  -7 .
The last term, "the constant", is  -10 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -10 = -120 

Step-2 : Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  8 
                     12m² - 15m + 8m - 10

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

Final result :

  3 • (4m - 5) • (3m + 2)