Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  23x2) -  29x) +  12

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -8x² - 29x + 12  =   -1 • (8x² + 29x - 12) 

Trying to factor by splitting the middle term

 3.2     Factoring  8x² + 29x - 12 

The first term is,  8x²  its coefficient is  8 .
The middle term is,  +29x  its coefficient is  29 .
The last term, "the constant", is  -12 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -12 = -96 

Step-2 : Find two factors of  -96  whose sum equals the coefficient of the middle term, which is   29 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  32 
                     8x² - 3x + 32x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (8x-3)
              Add up the last 2 terms, pulling out common factors :
                    4 • (8x-3)
Step-5 : Add up the four terms of step 4 :
                    (x+4)  •  (8x-3)
             Which is the desired factorization

Final result :

  (3 - 8x) • (x + 4)