Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3n2) -  17n) -  40

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  12n²-17n-40 

The first term is,  12n²  its coefficient is  12 .
The middle term is,  -17n  its coefficient is  -17 .
The last term, "the constant", is  -40 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -40 = -480 

Step-2 : Find two factors of  -480  whose sum equals the coefficient of the middle term, which is   -17 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -32  and  15 
                     12n² - 32n + 15n - 40

Step-4 : Add up the first 2 terms, pulling out like factors :
                    4n • (3n-8)
              Add up the last 2 terms, pulling out common factors :
                    5 • (3n-8)
Step-5 : Add up the four terms of step 4 :
                    (4n+5)  •  (3n-8)
             Which is the desired factorization

Final result :

  (3n - 8) • (4n + 5)