To solve the equation \((x + 7)(x - 3) = 0\), we can set each factor equal to zero:
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\(x + 7 = 0\) \[ x = -7 \]
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\(x - 3 = 0\) \[ x = 3 \]
Thus, the solutions are \(x = -7\) and \(x = 3\).
Listing the smaller solution first, we have: \[ x = -7 \text{ and } x = 3 \]