Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (23a2 +  18a) -  5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  8a²+18a-5 

The first term is,  8a²  its coefficient is  8 .
The middle term is,  +18a  its coefficient is  18 .
The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -5 = -40 

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   18 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  20 
                     8a² - 2a + 20a - 5

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

Final result :

  (4a - 1) • (2a + 5)