Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((5x2 -  6x) +  5x) +  12

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²-x+12 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  +12 

Step-1 : Multiply the coefficient of the first term by the constant   5 • 12 = 60 

Step-2 : Find two factors of  60  whose sum equals the coefficient of the middle term, which is   -1 .

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 :

  5x2 - x + 12