$$ \begin{aligned} \frac{4}{7}(14t+3t+4) &= 0&& \text{simplify left side} \\[1 em]\frac{4}{7}(17t+4) &= 0&& \\[1 em]\frac{68t+16}{7} &= 0&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{68t+16}{7} &= 7\cdot0&& \text{cancel out the denominators} \\[1 em]68t+16 &= 0&& \text{ move the constants to the right } \\[1 em]68t &= -16&& \text{ divide both sides by $ 68 $ } \\[1 em]t &= -\frac{16}{68}&& \\[1 em]t &= -\frac{4}{17}&& \\[1 em] \end{aligned} $$

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