Question
$$\frac{6}{s^3+14s^2+85s+500} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{6}{s^3+14s^2+85s+500} &= 0&& \text{multiply ALL terms by } \color{blue}{ s^3+14s^2+85s+500 }. \\[1 em](s^3+14s^2+85s+500)\cdot\frac{6}{s^3+14s^2+85s+500} &= (s^3+14s^2+85s+500)\cdot0&& \text{cancel out the denominators} \\[1 em]6 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 6 = 0 } $ is FALSE, we conclude that the equation has no solution.
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