The given polynomial equation is
\[ -x^{3}-2x^{2}+8x=0 \]
Factoring this polynomial yields:
\[ -x \left(x - 2\right) \left(x + 4\right) = 0 \]
To find the values of \( x \), we set each factor equal to zero:
The solutions obtained are:
\[ x = -4, \quad x = 0, \quad x = 2 \]
Sorting these solutions gives:
The smallest solution is
\[ \boxed{x = -4} \]
The complete set of solutions is
\[ \boxed{x = -4, 0, 2} \]
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