Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2n2 -  5n) -  42

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2n²-5n-42 

The first term is,  2n²  its coefficient is  2 .
The middle term is,  -5n  its coefficient is  -5 .
The last term, "the constant", is  -42 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -42 = -84 

Step-2 : Find two factors of  -84  whose sum equals the coefficient of the middle term, which is   -5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  7 
                     2n² - 12n + 7n - 42

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2n • (n-6)
              Add up the last 2 terms, pulling out common factors :
                    7 • (n-6)
Step-5 : Add up the four terms of step 4 :
                    (2n+7)  •  (n-6)
             Which is the desired factorization

Final result :

  (n - 6) • (2n + 7)