Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((3•5m2) +  16m) -  15

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  15m²+16m-15 

The first term is,  15m²  its coefficient is  15 .
The middle term is,  +16m  its coefficient is  16 .
The last term, "the constant", is  -15 

Step-1 : Multiply the coefficient of the first term by the constant   15 • -15 = -225 

Step-2 : Find two factors of  -225  whose sum equals the coefficient of the middle term, which is   16 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  25 
                     15m² - 9m + 25m - 15

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

Final result :

  (5m - 3) • (3m + 5)