Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (52x2 -  750x) -  4500

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   25x² - 750x - 4500  =   25 • (x² - 30x - 180) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - 30x - 180 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -30x  its coefficient is  -30 .
The last term, "the constant", is  -180 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -180 = -180 

Step-2 : Find two factors of  -180  whose sum equals the coefficient of the middle term, which is   -30 .

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  25 • (x2 - 30x - 180)