Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  2t2) +  13t) -  15

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -2t² + 13t - 15  =   -1 • (2t² - 13t + 15) 

Trying to factor by splitting the middle term

 3.2     Factoring  2t² - 13t + 15 

The first term is,  2t²  its coefficient is  2 .
The middle term is,  -13t  its coefficient is  -13 .
The last term, "the constant", is  +15 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 15 = 30 

Step-2 : Find two factors of  30  whose sum equals the coefficient of the middle term, which is   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  -3 
                     2t² - 10t - 3t - 15

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

Final result :

  (5 - t) • (2t - 3)