$$ \begin{aligned} 5(9x+3)+4-9x &= \frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot5(9x+3)+3\cdot4-3\cdot9x &= 3\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]135x+45+12-27x &= 1&& \text{simplify left side} \\[1 em]108x+57 &= 1&& \text{ move 57 to the right } \\[1 em]108x &= 1-57&& \\[1 em]108x &= -56&& \text{ divide both sides by $ 108 $ } \\[1 em]x &= -\frac{56}{108}&& \\[1 em]x &= -\frac{14}{27}&& \\[1 em] \end{aligned} $$

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