Question
$$3x^2 = 75x^4$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{ 1 }{ 5 } & x_3 = -\dfrac{ 1 }{ 5 } \end{matrix} $$
Explanation
$$ \begin{aligned} 3x^2 &= 75x^4&& \text{move all terms to the left hand side } \\[1 em]3x^2-75x^4 &= 0&& \text{simplify left side} \\[1 em]-75x^4+3x^2 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -75x^{4}+3x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ -75x^{4}+3x^{2} = x^2 \left( -75x^{2}+3 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ -75x^{2}+3 = 0$.
$ -75x^{2}+3 = 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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