Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3n2 -  11n) -  874

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3n²-11n-874 

The first term is,  3n²  its coefficient is  3 .
The middle term is,  -11n  its coefficient is  -11 .
The last term, "the constant", is  -874 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -874 = -2622 

Step-2 : Find two factors of  -2622  whose sum equals the coefficient of the middle term, which is   -11 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -57  and  46 
                     3n² - 57n + 46n - 874

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3n • (n-19)
              Add up the last 2 terms, pulling out common factors :
                    46 • (n-19)
Step-5 : Add up the four terms of step 4 :
                    (3n+46)  •  (n-19)
             Which is the desired factorization

Final result :

  (n - 19) • (3n + 46)