Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (1 - 12x) -  (32•5x2)

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -45x² - 12x + 1  =   -1 • (45x² + 12x - 1) 

Trying to factor by splitting the middle term

 3.2     Factoring  45x² + 12x - 1 

The first term is,  45x²  its coefficient is  45 .
The middle term is,  +12x  its coefficient is  12 .
The last term, "the constant", is  -1 

Step-1 : Multiply the coefficient of the first term by the constant   45 • -1 = -45 

Step-2 : Find two factors of  -45  whose sum equals the coefficient of the middle term, which is   12 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  15 
                     45x² - 3x + 15x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3x • (15x-1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (15x-1)
Step-5 : Add up the four terms of step 4 :
                    (3x+1)  •  (15x-1)
             Which is the desired factorization

Final result :

  (1 - 15x) • (3x + 1)