Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  3t2) +  11t) -  6

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -3t² + 11t - 6  =   -1 • (3t² - 11t + 6) 

Trying to factor by splitting the middle term

 3.2     Factoring  3t² - 11t + 6 

The first term is,  3t²  its coefficient is  3 .
The middle term is,  -11t  its coefficient is  -11 .
The last term, "the constant", is  +6 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 6 = 18 

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   -11 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -2 
                     3t² - 9t - 2t - 6

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

Final result :

  (3 - t) • (3t - 2)