Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (480 - 68a) +  2a2

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2a² - 68a + 480  =   2 • (a² - 34a + 240) 

Trying to factor by splitting the middle term

 3.2     Factoring  a² - 34a + 240 

The first term is,  a²  its coefficient is  1 .
The middle term is,  -34a  its coefficient is  -34 .
The last term, "the constant", is  +240 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 240 = 240 

Step-2 : Find two factors of  240  whose sum equals the coefficient of the middle term, which is   -34 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -24  and  -10 
                     a² - 24a - 10a - 240

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (a-24)
              Add up the last 2 terms, pulling out common factors :
                    10 • (a-24)
Step-5 : Add up the four terms of step 4 :
                    (a-10)  •  (a-24)
             Which is the desired factorization

Final result :

  2 • (a - 10) • (a - 24)