$$ \begin{aligned} 4(3x+1)-9 &= 5(3x-1)&& \text{simplify left and right hand side} \\[1 em]12x+4-9 &= 15x-5&& \\[1 em]12x-5 &= 15x-5&& \text{move the $ \color{blue}{ 15x } $ to the left side and $ \color{blue}{ -5 }$ to the right} \\[1 em]12x-15x &= -5+5&& \text{simplify left and right hand side} \\[1 em]-3x &= 0&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= \frac{0}{-3}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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