$$ \begin{aligned} 5x+6 &= 3-(4x+12)&& \text{simplify right side} \\[1 em]5x+6 &= 3-4x-12&& \\[1 em]5x+6 &= -4x-9&& \text{move the $ \color{blue}{ -4x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]5x+4x &= -9-6&& \text{simplify left and right hand side} \\[1 em]9x &= -15&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= -\frac{15}{9}&& \\[1 em]x &= -\frac{5}{3}&& \\[1 em] \end{aligned} $$

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