To solve the factored quadratic equation \((x - 5)(x + 3) = 0\), we can set each factor equal to zero.
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Set the first factor equal to zero: \[ x - 5 = 0 \implies x = 5 \]
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Set the second factor equal to zero: \[ x + 3 = 0 \implies x = -3 \]
The solutions are \(x = 5\) and \(x = -3\).
The smaller solution is \(x = -3\), and the larger solution is \(x = 5\).