Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x3"   was replaced by   "x^3". 

Step  1  :

Equation at the end of step  1  :

  128 -  (2•53x3)

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   128 - 250x³  =   -2 • (125x³ - 64) 

Trying to factor as a Difference of Cubes:

 3.2      Factoring:  125x³ - 64 

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into
              (a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =
            a³+a²b+ab²-ba²-b²a-b³ =
            a³+(a²b-ba²)+(ab²-b²a)-b³ =
            a³+0+0-b³ =
            a³-b³

Check :  125  is the cube of  5 

Check :  64  is the cube of   4 
Check :  x³ is the cube of   x¹

Factorization is :
             (5x - 4)  •  (25x² + 20x + 16) 

Trying to factor by splitting the middle term

 3.3     Factoring  25x² + 20x + 16 

The first term is,  25x²  its coefficient is  25 .
The middle term is,  +20x  its coefficient is  20 .
The last term, "the constant", is  +16 

Step-1 : Multiply the coefficient of the first term by the constant   25 • 16 = 400 

Step-2 : Find two factors of  400  whose sum equals the coefficient of the middle term, which is   20 .

For tidiness, printing of 24 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 :

  -2 • (5x - 4) • (25x2 + 20x + 16)