Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3x2) +  47x) -  4

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  12x²+47x-4 

The first term is,  12x²  its coefficient is  12 .
The middle term is,  +47x  its coefficient is  47 .
The last term, "the constant", is  -4 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -4 = -48 

Step-2 : Find two factors of  -48  whose sum equals the coefficient of the middle term, which is   47 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  48 
                     12x² - 1x + 48x - 4

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (12x-1)
              Add up the last 2 terms, pulling out common factors :
                    4 • (12x-1)
Step-5 : Add up the four terms of step 4 :
                    (x+4)  •  (12x-1)
             Which is the desired factorization

Final result :

  (12x - 1) • (x + 4)