Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x2 -  13x) +  12

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3x²-13x+12 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  -13x  its coefficient is  -13 .
The last term, "the constant", is  +12 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 12 = 36 

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -4 
                     3x² - 9x - 4x - 12

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

Final result :

  (x - 3) • (3x - 4)