Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22t2 -  10t) -  14

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4t² - 10t - 14  =   2 • (2t² - 5t - 7) 

Trying to factor by splitting the middle term

 3.2     Factoring  2t² - 5t - 7 

The first term is,  2t²  its coefficient is  2 .
The middle term is,  -5t  its coefficient is  -5 .
The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -7 = -14 

Step-2 : Find two factors of  -14  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,  -7  and  2 
                     2t² - 7t + 2t - 7

Step-4 : Add up the first 2 terms, pulling out like factors :
                    t • (2t-7)
              Add up the last 2 terms, pulling out common factors :
                     1 • (2t-7)
Step-5 : Add up the four terms of step 4 :
                    (t+1)  •  (2t-7)
             Which is the desired factorization

Final result :

  2 • (2t - 7) • (t + 1)