Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 +  6x) -  40

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4x² + 6x - 40  =   2 • (2x² + 3x - 20) 

Trying to factor by splitting the middle term

 3.2     Factoring  2x² + 3x - 20 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  +3x  its coefficient is  3 .
The last term, "the constant", is  -20 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -20 = -40 

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  8 
                     2x² - 5x + 8x - 20

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

Final result :

  2 • (2x - 5) • (x + 4)