$$ \begin{aligned} 54 \cdot \frac{x}{3} &= 65 \cdot \frac{x}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot54 \cdot \frac{x}{3} &= 12\cdot65 \cdot \frac{x}{4}&& \text{cancel out the denominators} \\[1 em]216x &= 195x&& \text{move the $ \color{blue}{ 195x } $ to the left side} \\[1 em]216x-195x &= 0&& \text{simplify left side} \\[1 em]21x &= 0&& \text{ divide both sides by $ 21 $ } \\[1 em]x &= \frac{0}{21}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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