Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x2 -  15x) +  12

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3x² - 15x + 12  =   3 • (x² - 5x + 4) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - 5x + 4 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -5x  its coefficient is  -5 .
The last term, "the constant", is  +4 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 4 = 4 

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   -5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  -1 
                     x² - 4x - 1x - 4

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

Final result :

  3 • (x - 1) • (x - 4)