2B. Solve the equation $x^{3}+(k-1) x^{2}-k x=0$, if its solutions are consecutive terms of an arithmetic progression.

保留源文本的换行和格式，这里直接输出翻译结果，但根据要求，实际上已经进行了翻译并保持了格式。如果有任何进一步的格式要求，请告知。
Solution. The solutions to the equation are $0,1,-k$. From the fact that they are consecutive terms of an arithmetic progression, it follows that $k \neq 0,-1$. This means the equation has three distinct real solutions that satisfy the conditions of the problem. If $k \in(-\infty,-1)$, then $-k>1$, so the order of the roots is $0,1,-k$. The difference of the arithmetic progression will be $1-0=1$, so $-k=2$, i.e., $k=-2$.

If $k \in(-1,0)$, then $-k \in(0,1)$, so the order of the roots is $0,-k, 1$. From $-k-0=1-(-k)$ we get $k=-\frac{1}{2}$, i.e., $-k=\frac{1}{2}$. If $k \in(0, \infty)$, then $-k \in(-\infty, 0)$, so the order is $-k, 0,1$. In this case, the progression has a difference of 1, so $-k=-1$.