Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3a2) -  17a) -  5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  12a²-17a-5 

The first term is,  12a²  its coefficient is  12 .
The middle term is,  -17a  its coefficient is  -17 .
The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -5 = -60 

Step-2 : Find two factors of  -60  whose sum equals the coefficient of the middle term, which is   -17 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  3 
                     12a² - 20a + 3a - 5

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

Final result :

  (3a - 5) • (4a + 1)