Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2c2 -  20c) +  18

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2c² - 20c + 18  =   2 • (c² - 10c + 9) 

Trying to factor by splitting the middle term

 3.2     Factoring  c² - 10c + 9 

The first term is,  c²  its coefficient is  1 .
The middle term is,  -10c  its coefficient is  -10 .
The last term, "the constant", is  +9 

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

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   -10 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -1 
                     c² - 9c - 1c - 9

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

Final result :

  2 • (c - 1) • (c - 9)