Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (23x2 -  19x) -  15

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  8x²-19x-15 

The first term is,  8x²  its coefficient is  8 .
The middle term is,  -19x  its coefficient is  -19 .
The last term, "the constant", is  -15 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -15 = -120 

Step-2 : Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   -19 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -24  and  5 
                     8x² - 24x + 5x - 15

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

Final result :

  (x - 3) • (8x + 5)