$$ \begin{aligned} \frac{1}{4}k &= 3(-\frac{1}{4}k+3)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{4}k &= 4\cdot3(-\frac{1}{4}k+3)&& \text{cancel out the denominators} \\[1 em]k &= 4\cdot3(-\frac{1}{4}k+3)&& \text{simplify right side} \\[1 em]k &= 12(-\frac{1}{4}k+3)&& \\[1 em]k &= 12(-\frac{k}{4}+3)&& \\[1 em]k &= 12 \cdot \frac{-k+12}{4}&& \\[1 em]k &= \frac{-12k+144}{4}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot1k &= 4 \cdot \frac{-12k+144}{4}&& \text{cancel out the denominators} \\[1 em]4k &= -12k+144&& \text{move the $ \color{blue}{ -12k } $ to the left side} \\[1 em]4k+12k &= 144&& \text{simplify left side} \\[1 em]16k &= 144&& \text{ divide both sides by $ 16 $ } \\[1 em]k &= \frac{144}{16}&& \\[1 em]k &= 9&& \\[1 em] \end{aligned} $$

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