Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  23x2) +  2x) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  -8x²+2x+1 

The first term is,  -8x²  its coefficient is  -8 .
The middle term is,  +2x  its coefficient is  2 .
The last term, "the constant", is  +1 

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

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

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

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

Final result :

  (4x + 1) • (1 - 2x)