Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (23x2 +  45x) -  18

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  8x²+45x-18 

The first term is,  8x²  its coefficient is  8 .
The middle term is,  +45x  its coefficient is  45 .
The last term, "the constant", is  -18 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -18 = -144 

Step-2 : Find two factors of  -144  whose sum equals the coefficient of the middle term, which is   45 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  48 
                     8x² - 3x + 48x - 18

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (8x-3)
              Add up the last 2 terms, pulling out common factors :
                    6 • (8x-3)
Step-5 : Add up the four terms of step 4 :
                    (x+6)  •  (8x-3)
             Which is the desired factorization

Final result :

  (8x - 3) • (x + 6)