Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  (2•32r2)) +  45r) +  8

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  -18r²+45r+8 

The first term is,  -18r²  its coefficient is  -18 .
The middle term is,  +45r  its coefficient is  45 .
The last term, "the constant", is  +8 

Step-1 : Multiply the coefficient of the first term by the constant   -18 • 8 = -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 
                     -18r² - 3r + 48r + 8

Step-4 : Add up the first 2 terms, pulling out like factors :
                    -3r • (6r+1)
              Add up the last 2 terms, pulling out common factors :
                    8 • (6r+1)
Step-5 : Add up the four terms of step 4 :
                    (-3r+8)  •  (6r+1)
             Which is the desired factorization

Final result :

  (6r + 1) • (8 - 3r)