Question
$$5\cdot(-1)^2+4\cdot(-1) = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 5\cdot(-1)^2+4\cdot(-1) &= 0&& \text{simplify left side} \\[1 em]5\cdot(-1)^2+(-4) &= 0&& \\[1 em]5\cdot1+(-4) &= 0&& \\[1 em]5\cdot1+(-4) &= 0&& \\[1 em]1 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 1 = 0 } $ is FALSE, we conclude that the equation has no solution.
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