Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  83115 -  ((22x3 • 1160) • a)

Step  2  :

Multiplying exponents :

 2.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Equation at the end of step  2  :

  83115 -  ((25•5•29x3) • a)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   83115 - 4640x³a  =   -5 • (928x³a - 16623) 

Trying to factor as a Difference of Cubes:

 4.2      Factoring:  928x³a - 16623 

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 :  928  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  -5 • (928x3a - 16623)