Question
$$30x^6+40x^5+6x^4 = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -\dfrac{ 2 }{ 3 }-\dfrac{\sqrt{ 55 }}{ 15 } & x_3 = -\dfrac{ 2 }{ 3 }+\dfrac{\sqrt{ 55 }}{ 15 } \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ 30x^{6}+40x^{5}+6x^{4} = 0 } $, first we need to factor our $ x^4 $.
$$ 30x^{6}+40x^{5}+6x^{4} = x^4 \left( 30x^{2}+40x+6 \right) $$$ x = 0 $ is a root of multiplicity $ 4 $.
The remaining roots can be found by solving equation $ 30x^{2}+40x+6 = 0$.
$ 30x^{2}+40x+6 = 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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