$$ \begin{aligned} x\cdot\frac{2}{3}-9x\cdot\frac{1}{3}+14 &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3x\cdot\frac{2}{3}-39x\cdot\frac{1}{3}+3\cdot14 &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]2x-9x+42 &= 0&& \text{simplify left side} \\[1 em]-7x+42 &= 0&& \text{ move the constants to the right } \\[1 em]-7x &= -42&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= \frac{-42}{-7}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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