Question
$$\frac{2}{6x^2} = \frac{3x+8}{6x^2}$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -2 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2}{6x^2} &= \frac{3x+8}{6x^2}&& \text{multiply ALL terms by } \color{blue}{ 6x^2 }. \\[1 em]6x^2\cdot\frac{2}{6x^2} &= 6x^2\frac{3x+8}{6x^2}&& \text{cancel out the denominators} \\[1 em]2x^4 &= 3x^5+8x^4&& \text{move all terms to the left hand side } \\[1 em]2x^4-3x^5-8x^4 &= 0&& \text{simplify left side} \\[1 em]-3x^5-6x^4 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -3x^{5}-6x^{4} = 0 } $, first we need to factor our $ x^4 $.
$$ -3x^{5}-6x^{4} = x^4 \left( -3x-6 \right) $$$ x = 0 $ is a root of multiplicity $ 4 $.
The second root can be found by solving equation $ -3x-6 = 0$.
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