Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  23x2) -  15x) +  2

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -8x² - 15x + 2  =   -1 • (8x² + 15x - 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  8x² + 15x - 2 

The first term is,  8x²  its coefficient is  8 .
The middle term is,  +15x  its coefficient is  15 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -2 = -16 

Step-2 : Find two factors of  -16  whose sum equals the coefficient of the middle term, which is   15 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  16 
                     8x² - 1x + 16x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (8x-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (8x-1)
Step-5 : Add up the four terms of step 4 :
                    (x+2)  •  (8x-1)
             Which is the desired factorization

Final result :

  (1 - 8x) • (x + 2)