$$ \begin{aligned} 9(x+3) &= 4x-3&& \text{simplify left side} \\[1 em]9x+27 &= 4x-3&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 27 }$ to the right} \\[1 em]9x-4x &= -3-27&& \text{simplify left and right hand side} \\[1 em]5x &= -30&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{30}{5}&& \\[1 em]x &= -6&& \\[1 em] \end{aligned} $$

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