Question
$$12(x+3) = 3(4x-5)+9$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 12(x+3) &= 3(4x-5)+9&& \text{simplify left and right hand side} \\[1 em]12x+36 &= 12x-15+9&& \\[1 em]12x+36 &= 12x-6&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 36 }$ to the right} \\[1 em]12x-12x &= -6-36&& \text{simplify left and right hand side} \\[1 em]12x-12x &= -42&& \\[1 em]0 &= -42&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -42 } $ is FALSE, we conclude that the equation has no solution.
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