Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  3x2) +  12x) +  6

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -3x² + 12x + 6  =   -3 • (x² - 4x - 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - 4x - 2 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -4x  its coefficient is  -4 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2 = -2 

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   -4 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  -3 • (x2 - 4x - 2)