Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2x2 -  x) -  21

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2x²-x-21 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -21 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -21 = -42 

Step-2 : Find two factors of  -42  whose sum equals the coefficient of the middle term, which is   -1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  6 
                     2x² - 7x + 6x - 21

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (2x-7)
              Add up the last 2 terms, pulling out common factors :
                    3 • (2x-7)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (2x-7)
             Which is the desired factorization

Final result :

  (2x - 7) • (x + 3)