$$ \begin{aligned} 5x+6-3(x+1) &= 9x+6&& \text{simplify left side} \\[1 em]5x+6-(3x+3) &= 9x+6&& \\[1 em]5x+6-3x-3 &= 9x+6&& \\[1 em]2x+3 &= 9x+6&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]2x-9x &= 6-3&& \text{simplify left and right hand side} \\[1 em]-7x &= 3&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= -\frac{3}{7}&& \\[1 em] \end{aligned} $$

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