Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  3x2) +  45x) -  78

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -3x² + 45x - 78  =   -3 • (x² - 15x + 26) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - 15x + 26 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -15x  its coefficient is  -15 .
The last term, "the constant", is  +26 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 26 = 26 

Step-2 : Find two factors of  26  whose sum equals the coefficient of the middle term, which is   -15 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -13  and  -2 
                     x² - 13x - 2x - 26

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-13)
              Add up the last 2 terms, pulling out common factors :
                    2 • (x-13)
Step-5 : Add up the four terms of step 4 :
                    (x-2)  •  (x-13)
             Which is the desired factorization

Final result :

  -3 • (x - 2) • (x - 13)