Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  3x2) +  17x) -  20

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -3x² + 17x - 20  =   -1 • (3x² - 17x + 20) 

Trying to factor by splitting the middle term

 3.2     Factoring  3x² - 17x + 20 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  -17x  its coefficient is  -17 .
The last term, "the constant", is  +20 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 20 = 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,  -12  and  -5 
                     3x² - 12x - 5x - 20

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

Final result :

  (4 - x) • (3x - 5)