$$(k^4-9)(k^2-1) = 0$$
Answer
$$ \begin{matrix}k_1 = 1 & k_2 = -1 & k_3 = 1.73205 \\[1 em] k_4 = -1.73205 & k_5 = 1.73205i & k_6 = -1.73205i \end{matrix} $$
Explanation
$$ \begin{aligned} (k^4-9)(k^2-1) &= 0&& \text{simplify left side} \\[1 em]k^6-k^4-9k^2+9 &= 0&& \\[1 em] \end{aligned} $$
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