$$ \begin{aligned} (3x+2)\cdot2 &= 4x+3&& \text{simplify left side} \\[1 em]6x+4 &= 4x+3&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]6x-4x &= 3-4&& \text{simplify left and right hand side} \\[1 em]2x &= -1&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{1}{2}&& \\[1 em] \end{aligned} $$
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