Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (10x + 10) -  ((7x2 +  5x) -  8)

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  -7x²+5x+18 

The first term is,  -7x²  its coefficient is  -7 .
The middle term is,  +5x  its coefficient is  5 .
The last term, "the constant", is  +18 

Step-1 : Multiply the coefficient of the first term by the constant   -7 • 18 = -126 

Step-2 : Find two factors of  -126  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,  -9  and  14 
                     -7x² - 9x + 14x + 18

Step-4 : Add up the first 2 terms, pulling out like factors :
                    -x • (7x+9)
              Add up the last 2 terms, pulling out common factors :
                    2 • (7x+9)
Step-5 : Add up the four terms of step 4 :
                    (-x+2)  •  (7x+9)
             Which is the desired factorization

Final result :

  (7x + 9) • (2 - x)