Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2x2 +  5x) -  42

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2x²+5x-42 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  +5x  its coefficient is  5 .
The last term, "the constant", is  -42 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -42 = -84 

Step-2 : Find two factors of  -84  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  12 
                     2x² - 7x + 12x - 42

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (2x-7)
              Add up the last 2 terms, pulling out common factors :
                    6 • (2x-7)
Step-5 : Add up the four terms of step 4 :
                    (x+6)  •  (2x-7)
             Which is the desired factorization

Final result :

  (2x - 7) • (x + 6)