Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (32r2 -  36r) -  45

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   9r² - 36r - 45  =   9 • (r² - 4r - 5) 

Trying to factor by splitting the middle term

 3.2     Factoring  r² - 4r - 5 

The first term is,  r²  its coefficient is  1 .
The middle term is,  -4r  its coefficient is  -4 .
The last term, "the constant", is  -5 

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

Step-2 : Find two factors of  -5  whose sum equals the coefficient of the middle term, which is   -4 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  1 
                     r² - 5r + 1r - 5

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

Final result :

  9 • (r + 1) • (r - 5)