$$ \begin{aligned} \frac{1}{3}t+\frac{3}{5} &= \frac{2}{5}-t&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{1}{3}t+15\cdot\frac{3}{5} &= 15\cdot\frac{2}{5}-15t&& \text{cancel out the denominators} \\[1 em]5t+9 &= 6-15t&& \text{move the $ \color{blue}{ -15t } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]5t+15t &= 6-9&& \text{simplify left and right hand side} \\[1 em]20t &= -3&& \text{ divide both sides by $ 20 $ } \\[1 em]t &= -\frac{3}{20}&& \\[1 em] \end{aligned} $$

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