$$ \begin{aligned} \frac{x}{216}+\frac{125}{216}-300\frac{x}{253} &= 0&& \text{multiply ALL terms by } \color{blue}{ 54648 }. \\[1 em]54648 \cdot \frac{x}{216}+54648\cdot\frac{125}{216}-54648\cdot300\frac{x}{253} &= 54648\cdot0&& \text{cancel out the denominators} \\[1 em]253x+31625-64800x &= 0&& \text{simplify left side} \\[1 em]-64547x+31625 &= 0&& \text{ move the constants to the right } \\[1 em]-64547x &= -31625&& \text{ divide both sides by $ -64547 $ } \\[1 em]x &= \frac{-31625}{-64547}&& \\[1 em]x &= \frac{31625}{64547}&& \\[1 em] \end{aligned} $$

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