Question
$$-5x^3-3x^5 = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{\sqrt{ 15 }}{ 3 } i & x_3 = - \dfrac{\sqrt{ 15 }}{ 3 } i \end{matrix} $$
Explanation
$$ \begin{aligned} -5x^3-3x^5 &= 0&& \text{simplify left side} \\[1 em]-3x^5-5x^3 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -3x^{5}-5x^{3} = 0 } $, first we need to factor our $ x^3 $.
$$ -3x^{5}-5x^{3} = x^3 \left( -3x^{2}-5 \right) $$$ x = 0 $ is a root of multiplicity $ 3 $.
The remaining roots can be found by solving equation $ -3x^{2}-5 = 0$.
$ -3x^{2}-5 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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