Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2t2 +  7t) +  6

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2t²+7t+6 

The first term is,  2t²  its coefficient is  2 .
The middle term is,  +7t  its coefficient is  7 .
The last term, "the constant", is  +6 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 6 = 12 

Step-2 : Find two factors of  12  whose sum equals the coefficient of the middle term, which is   7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  4 
                     2t² + 3t + 4t + 6

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

Final result :

  (2t + 3) • (t + 2)