Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((23•7x2) -  15x) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  56x²-15x+1 

The first term is,  56x²  its coefficient is  56 .
The middle term is,  -15x  its coefficient is  -15 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   56 • 1 = 56 

Step-2 : Find two factors of  56  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,  -8  and  -7 
                     56x² - 8x - 7x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    8x • (7x-1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (7x-1)
Step-5 : Add up the four terms of step 4 :
                    (8x-1)  •  (7x-1)
             Which is the desired factorization

Final result :

  (7x - 1) • (8x - 1)