Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3n2 +  15n) -  12

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3n² + 15n - 12  =   3 • (n² + 5n - 4) 

Trying to factor by splitting the middle term

 3.2     Factoring  n² + 5n - 4 

The first term is,  n²  its coefficient is  1 .
The middle term is,  +5n  its coefficient is  5 .
The last term, "the constant", is  -4 

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

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   5 .

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

Final result :

  3 • (n2 + 5n - 4)