Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (32x2 -  43x) -  10

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  9x²-43x-10 

The first term is,  9x²  its coefficient is  9 .
The middle term is,  -43x  its coefficient is  -43 .
The last term, "the constant", is  -10 

Step-1 : Multiply the coefficient of the first term by the constant   9 • -10 = -90 

Step-2 : Find two factors of  -90  whose sum equals the coefficient of the middle term, which is   -43 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -45  and  2 
                     9x² - 45x + 2x - 10

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

Final result :

  (x - 5) • (9x + 2)