Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  t²+5t+6 

The first term is,  t²  its coefficient is  1 .
The middle term is,  +5t  its coefficient is  5 .
The last term, "the constant", is  +6 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 6 = 6 

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  3 
                     t² + 2t + 3t + 6

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

Final result :

  (t + 3) • (t + 2)