$$ \begin{aligned} 15 &= \frac{2}{3}(2x+15)&& \text{simplify right side} \\[1 em]15 &= \frac{4x+30}{3}&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot15 &= 3 \cdot \frac{4x+30}{3}&& \text{cancel out the denominators} \\[1 em]45 &= 4x+30&& \text{ swap the left and right side of the equation } \\[1 em]4x+30 &= 45&& \text{ move 30 to the right } \\[1 em]4x &= 45-30&& \\[1 em]4x &= 15&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{15}{4}&& \\[1 em] \end{aligned} $$

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