$$s^4+7s^3+16s^2+8s = 0$$
Answer
$$ \begin{matrix}s_1 = 0 & s_2 = -0.6854 & s_3 = -3.1573+1.30515i \\[1 em] s_4 = -3.1573-1.30515i & \\[1 em] \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ x^{4}+7x^{3}+16x^{2}+8x = 0 } $, first we need to factor our $ x $.
$$ x^{4}+7x^{3}+16x^{2}+8x = x \left( x^{3}+7x^{2}+16x+8 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ x^{3}+7x^{2}+16x+8 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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