Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3x2) -  5x) -  21

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  6x²-5x-21 

The first term is,  6x²  its coefficient is  6 .
The middle term is,  -5x  its coefficient is  -5 .
The last term, "the constant", is  -21 

Step-1 : Multiply the coefficient of the first term by the constant   6 • -21 = -126 

Step-2 : Find two factors of  -126  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,  -14  and  9 
                     6x² - 14x + 9x - 21

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

Final result :

  (3x - 7) • (2x + 3)