Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22x2 -  3x) -  12x) +  9

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4x²-15x+9 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  -15x  its coefficient is  -15 .
The last term, "the constant", is  +9 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 9 = 36 

Step-2 : Find two factors of  36  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,  -12  and  -3 
                     4x² - 12x - 3x - 9

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

Final result :

  (x - 3) • (4x - 3)