Question
$$4(x+7) = 2(x+12)+2(x+1)$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 4(x+7) &= 2(x+12)+2(x+1)&& \text{simplify left and right hand side} \\[1 em]4x+28 &= 2x+24+2x+2&& \\[1 em]4x+28 &= 4x+26&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 28 }$ to the right} \\[1 em]4x-4x &= 26-28&& \text{simplify left and right hand side} \\[1 em]4x-4x &= -2&& \\[1 em]0 &= -2&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -2 } $ is FALSE, we conclude that the equation has no solution.
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