$$\frac{16}{7x}+\frac{2}{5} = \frac{2}{7}x$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -\dfrac{ 1 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{16}{7x}+\frac{2}{5} &= \frac{2}{7}x&& \text{multiply ALL terms by } \color{blue}{ 7x\cdot5 }. \\[1 em]7x\cdot5\cdot\frac{16}{7x}+7x\cdot5\cdot\frac{2}{5} &= 7x\cdot5 \cdot \frac{2}{7}x&& \text{cancel out the denominators} \\[1 em]80x^2+14x &= 10x^2&& \text{move all terms to the left hand side } \\[1 em]80x^2+14x-10x^2 &= 0&& \text{simplify left side} \\[1 em]70x^2+14x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 70x^{2}+14x = 0 } $, first we need to factor our $ x $.
$$ 70x^{2}+14x = x \left( 70x+14 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ 70x+14 = 0$.
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