Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x + 1) -  (2•32x2)

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  -18x²+3x+1 

The first term is,  -18x²  its coefficient is  -18 .
The middle term is,  +3x  its coefficient is  3 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   -18 • 1 = -18 

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  6 
                     -18x² - 3x + 6x + 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    -3x • (6x+1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (6x+1)
Step-5 : Add up the four terms of step 4 :
                    (-3x+1)  •  (6x+1)
             Which is the desired factorization

Final result :

  (6x + 1) • (1 - 3x)