Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (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) • (2x + 1)