To solve the factored quadratic equation \((13x + 3)(9x - 14) = 0\), we can set each factor to zero and solve for \(x\).
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Set the first factor to zero: \[ 13x + 3 = 0 \] Subtract 3 from both sides: \[ 13x = -3 \] Now, divide by 13: \[ x = -\frac{3}{13} \]
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Set the second factor to zero: \[ 9x - 14 = 0 \] Add 14 to both sides: \[ 9x = 14 \] Now, divide by 9: \[ x = \frac{14}{9} \]
Thus, the solution set is: \[ x = \left{ -\frac{3}{13}, \frac{14}{9} \right} \]
From the provided responses, the correct one is: The solution set is \( x = \left{ -\frac{3}{13}, \frac{14}{9} \right} \).