Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  5t2) +  11t) +  42

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  -5t²+11t+42 

The first term is,  -5t²  its coefficient is  -5 .
The middle term is,  +11t  its coefficient is  11 .
The last term, "the constant", is  +42 

Step-1 : Multiply the coefficient of the first term by the constant   -5 • 42 = -210 

Step-2 : Find two factors of  -210  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,  -10  and  21 
                     -5t² - 10t + 21t + 42

Step-4 : Add up the first 2 terms, pulling out like factors :
                    -5t • (t+2)
              Add up the last 2 terms, pulling out common factors :
                    21 • (t+2)
Step-5 : Add up the four terms of step 4 :
                    (-5t+21)  •  (t+2)
             Which is the desired factorization

Final result :

  (t + 2) • (21 - 5t)