Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3x2) -  21x) -  6

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   12x² - 21x - 6  =   3 • (4x² - 7x - 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  4x² - 7x - 2 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  -7x  its coefficient is  -7 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -2 = -8 

Step-2 : Find two factors of  -8  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  1 
                     4x² - 8x + 1x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    4x • (x-2)
              Add up the last 2 terms, pulling out common factors :
                     1 • (x-2)
Step-5 : Add up the four terms of step 4 :
                    (4x+1)  •  (x-2)
             Which is the desired factorization

Final result :

  3 • (x - 2) • (4x + 1)