$$ \begin{aligned} 6(-4x+3)+6 &= 4x-3(5x-9)&& \text{simplify left and right hand side} \\[1 em]-24x+18+6 &= 4x-(15x-27)&& \\[1 em]-24x+24 &= 4x-15x+27&& \\[1 em]-24x+24 &= -11x+27&& \text{move the $ \color{blue}{ -11x } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]-24x+11x &= 27-24&& \text{simplify left and right hand side} \\[1 em]-13x &= 3&& \text{ divide both sides by $ -13 $ } \\[1 em]x &= -\frac{3}{13}&& \\[1 em] \end{aligned} $$

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