$$ \begin{aligned} \frac{5x-6}{6x+6} &= \frac{10}{3}&& \text{multiply ALL terms by } \color{blue}{ (6x+6)\cdot3 }. \\[1 em](6x+6)\cdot3 \cdot \frac{5x-6}{6x+6} &= (6x+6)\cdot3\cdot\frac{10}{3}&& \text{cancel out the denominators} \\[1 em]15x-18 &= 60x+60&& \text{move the $ \color{blue}{ 60x } $ to the left side and $ \color{blue}{ -18 }$ to the right} \\[1 em]15x-60x &= 60+18&& \text{simplify left and right hand side} \\[1 em]-45x &= 78&& \text{ divide both sides by $ -45 $ } \\[1 em]x &= -\frac{78}{45}&& \\[1 em]x &= -\frac{26}{15}&& \\[1 em] \end{aligned} $$

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