Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 +  x) -  33

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4x²+x-33 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  +x  its coefficient is  1 .
The last term, "the constant", is  -33 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -33 = -132 

Step-2 : Find two factors of  -132  whose sum equals the coefficient of the middle term, which is   1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -11  and  12 
                     4x² - 11x + 12x - 33

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (4x-11)
              Add up the last 2 terms, pulling out common factors :
                    3 • (4x-11)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (4x-11)
             Which is the desired factorization

Final result :

  (4x - 11) • (x + 3)