Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (23x2 -  5x) -  3

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  8x²-5x-3 

The first term is,  8x²  its coefficient is  8 .
The middle term is,  -5x  its coefficient is  -5 .
The last term, "the constant", is  -3 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -3 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

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

Step-4 : Add up the first 2 terms, pulling out like factors :
                    8x • (x-1)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-1)
Step-5 : Add up the four terms of step 4 :
                    (8x+3)  •  (x-1)
             Which is the desired factorization

Final result :

  (x - 1) • (8x + 3)