$$ \begin{aligned} 15 &= \frac{3}{2}(2x+15)&& \text{simplify right side} \\[1 em]15 &= \frac{6x+45}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot15 &= 2 \cdot \frac{6x+45}{2}&& \text{cancel out the denominators} \\[1 em]30 &= 6x+45&& \text{ swap the left and right side of the equation } \\[1 em]6x+45 &= 30&& \text{ move 45 to the right } \\[1 em]6x &= 30-45&& \\[1 em]6x &= -15&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{15}{6}&& \\[1 em]x &= -\frac{5}{2}&& \\[1 em] \end{aligned} $$

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