Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  3x2) -  3x) +  126

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -3x² - 3x + 126  =   -3 • (x² + x - 42) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² + x - 42 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +x  its coefficient is  1 .
The last term, "the constant", is  -42 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -42 = -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,  -6  and  7 
                     x² - 6x + 7x - 42

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

Final result :

  -3 • (x + 7) • (x - 6)