Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (7 - 10x) -  23x2

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -8x² - 10x + 7  =   -1 • (8x² + 10x - 7) 

Trying to factor by splitting the middle term

 3.2     Factoring  8x² + 10x - 7 

The first term is,  8x²  its coefficient is  8 .
The middle term is,  +10x  its coefficient is  10 .
The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -7 = -56 

Step-2 : Find two factors of  -56  whose sum equals the coefficient of the middle term, which is   10 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  14 
                     8x² - 4x + 14x - 7

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

Final result :

  (1 - 2x) • (4x + 7)