Question 548753
Factoring leads you to the answer
{{{256n^3 = 30976n}}} ---> {{{256n^3-30976n=0}}} ---> {{{256n(n^2-121)=0}}} ---> {{{256n(n+11)(n-11)=0}}}
I just asked my calculator, and found that {{{30976/256=121}}}, so I pulled 256n out as a common factor. I guess I could have divided both sides of the equation by 256 at the start instead.
I recognized {{{n^2=121=n^2-11^2}}} as the difference of two squares after that.
The full factorization tells you that the solutions to the equation will be
{{{n=0}}}, {{{n=-11}}}, and {{{n=11}}}, the values that make the factors zero.