Answer:
 -4x2 + 3x - 225
  ———————————————
         3     
Step-by-step explanation:
Step  1  :
                4
Simplify   —
                 3
Equation at the end of step  1  :
         4            
  (x -  (— • x2)) -  75
         3            
Step  2  :
Equation at the end of step  2  :
        4x2      
  (x -  ———) -  75
         3      
Step  3  :
Rewriting the whole as an Equivalent Fraction :
 3.1   Subtracting a fraction from a whole
Rewrite the whole as a fraction using  3  as the denominator :
          x     x • 3
     x =  —  =  —————
          1       3  
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
 3.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
 x • 3 - (4x2)     3x - 4x2
 —————————————  =  ————————
       3              3    
Equation at the end of step  3  :
  (3x - 4x2)    
  —————————— -  75
      3          
Step  4  :
Rewriting the whole as an Equivalent Fraction :
 4.1   Subtracting a whole from a fraction
Rewrite the whole as a fraction using  3  as the denominator :
          75     75 • 3
    75 =  ——  =  ——————
          1        3    
Step  5  :
Pulling out like terms :
 5.1     Pull out like factors :
   3x - 4x2  =   -x • (4x - 3)  
Adding fractions that have a common denominator :
 5.2       Adding up the two equivalent fractions
 -x • (4x-3) - (75 • 3)     -4x2 + 3x - 225
 ——————————————————————  =  ———————————————
           3                       3        
Step  6  :
Pulling out like terms :
 6.1     Pull out like factors :
   -4x2 + 3x - 225  =   -1 • (4x2 - 3x + 225)  
Trying to factor by splitting the middle term
 6.2     Factoring  4x2 - 3x + 225  
The first term is,  4x2  its coefficient is  4 .
The middle term is,  -3x  its coefficient is  -3 .
The last term, "the constant", is  +225  
Step-1 : Multiply the coefficient of the first term by the constant   4 • 225 = 900  
Step-2 : Find two factors of  900  whose sum equals the coefficient of the middle term, which is   -3 .
      -900    +    -1    =    -901  
      -450    +    -2    =    -452  
      -300    +    -3    =    -303  
      -225    +    -4    =    -229  
      -180    +    -5    =    -185  
      -150    +    -6    =    -156  
For tidiness, printing of 48 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 :
  -4x2 + 3x - 225
  ———————————————
         3