Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

Step  2  :

            9t2 - 15t - 24
 Simplify   ——————————————
                  -3      

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   9t² - 15t - 24  =   3 • (3t² - 5t - 8) 

Trying to factor by splitting the middle term

 3.2     Factoring  3t² - 5t - 8 

The first term is,  3t²  its coefficient is  3 .
The middle term is,  -5t  its coefficient is  -5 .
The last term, "the constant", is  -8 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -8 = -24 

Step-2 : Find two factors of  -24  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,  -8  and  3 
                     3t² - 8t + 3t - 8

Step-4 : Add up the first 2 terms, pulling out like factors :
                    t • (3t-8)
              Add up the last 2 terms, pulling out common factors :
                     1 • (3t-8)
Step-5 : Add up the four terms of step 4 :
                    (t+1)  •  (3t-8)
             Which is the desired factorization

Final result :

  (8 - 3t) • (t + 1)