$$ \begin{aligned} 3x\cdot2+47(9x\cdot4-78)-1 &= 27\cdot(1+3x\cdot8)&& \text{simplify left and right hand side} \\[1 em]6x+47(36x-78)-1 &= 27\cdot(1+24x)&& \\[1 em]6x+1692x-3666-1 &= 27+648x&& \\[1 em]1698x-3666-1 &= 648x+27&& \\[1 em]1698x-3667 &= 648x+27&& \text{move the $ \color{blue}{ 648x } $ to the left side and $ \color{blue}{ -3667 }$ to the right} \\[1 em]1698x-648x &= 27+3667&& \text{simplify left and right hand side} \\[1 em]1050x &= 3694&& \text{ divide both sides by $ 1050 $ } \\[1 em]x &= \frac{3694}{1050}&& \\[1 em]x &= \frac{1847}{525}&& \\[1 em] \end{aligned} $$

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