Question
$$4(5x+8) = -20x+40x+4-4$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 4(5x+8) &= -20x+40x+4-4&& \text{simplify left and right hand side} \\[1 em]20x+32 &= -20x+40x+4-4&& \\[1 em]20x+32 &= 20x&& \text{move the $ \color{blue}{ 20x } $ to the left side and $ \color{blue}{ 32 }$ to the right} \\[1 em]20x-20x &= -32&& \text{simplify left side} \\[1 em]20x-20x &= -32&& \\[1 em]0 &= -32&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -32 } $ is FALSE, we conclude that the equation has no solution.
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