Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (52x2 -  95x) +  90

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   25x² - 95x + 90  =   5 • (5x² - 19x + 18) 

Trying to factor by splitting the middle term

 3.2     Factoring  5x² - 19x + 18 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -19x  its coefficient is  -19 .
The last term, "the constant", is  +18 

Step-1 : Multiply the coefficient of the first term by the constant   5 • 18 = 90 

Step-2 : Find two factors of  90  whose sum equals the coefficient of the middle term, which is   -19 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  -9 
                     5x² - 10x - 9x - 18

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

Final result :

  5 • (x - 2) • (5x - 9)