$$ \begin{aligned} 2\cdot(-20)+3 \cdot \frac{5}{4}x\cdot(-20)+5\frac{2}{5}x\cdot50+4x\cdot50 &= 0&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20\cdot2\cdot(-20)+20\cdot3 \cdot \frac{5}{4}x\cdot(-20)+20\cdot5\frac{2}{5}x\cdot50+204x\cdot50 &= 20\cdot0&& \text{cancel out the denominators} \\[1 em]-800-1500x+2000x+4000x &= 0&& \text{simplify left side} \\[1 em]4500x-800 &= 0&& \text{ move the constants to the right } \\[1 em]4500x &= 800&& \text{ divide both sides by $ 4500 $ } \\[1 em]x &= \frac{800}{4500}&& \\[1 em]x &= \frac{8}{45}&& \\[1 em] \end{aligned} $$

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