Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (32r2 -  2) -  17r

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  9r²-17r-2 

The first term is,  9r²  its coefficient is  9 .
The middle term is,  -17r  its coefficient is  -17 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   9 • -2 = -18 

Step-2 : Find two factors of  -18  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,  -18  and  1 
                     9r² - 18r + 1r - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    9r • (r-2)
              Add up the last 2 terms, pulling out common factors :
                     1 • (r-2)
Step-5 : Add up the four terms of step 4 :
                    (9r+1)  •  (r-2)
             Which is the desired factorization

Final result :

  (r - 2) • (9r + 1)