$$ \begin{aligned} \frac{100-4u}{3} &= \frac{5u+6}{4}+6&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{100-4u}{3} &= 12 \cdot \frac{5u+6}{4}+12\cdot6&& \text{cancel out the denominators} \\[1 em]-16u+400 &= 15u+18+72&& \text{simplify right side} \\[1 em]-16u+400 &= 15u+90&& \text{move the $ \color{blue}{ 15u } $ to the left side and $ \color{blue}{ 400 }$ to the right} \\[1 em]-16u-15u &= 90-400&& \text{simplify left and right hand side} \\[1 em]-31u &= -310&& \text{ divide both sides by $ -31 $ } \\[1 em]u &= \frac{-310}{-31}&& \\[1 em]u &= 10&& \\[1 em] \end{aligned} $$

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