Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (19x2 +  12) +  3x

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  19x²+3x+12 

The first term is,  19x²  its coefficient is  19 .
The middle term is,  +3x  its coefficient is  3 .
The last term, "the constant", is  +12 

Step-1 : Multiply the coefficient of the first term by the constant   19 • 12 = 228 

Step-2 : Find two factors of  228  whose sum equals the coefficient of the middle term, which is   3 .

For tidiness, printing of 18 lines which failed to find two such factors, was suppressed

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

Final result :

  19x2 + 3x + 12