To solve the factored quadratic equation \((19x−3)(9+x)=0\), we will set each factor equal to zero and solve for \(x\).
1. Set the first factor equal to zero:
\[
19x - 3 = 0
\]
Adding \(3\) to both sides gives:
\[
19x = 3
\]
Dividing both sides by \(19\) gives:
\[
x = \frac{3}{19}
\]
2. Set the second factor equal to zero:
\[
9 + x = 0
\]
Subtracting \(9\) from both sides gives:
\[
x = -9
\]
Now we have the two solutions:
\[
x = \frac{3}{19} \quad \text{and} \quad x = -9
\]
Thus, the solution set is:
\[
\left\{-9, \frac{3}{19}\right\}
\]
Since \(\frac{3}{19} \approx 0.158\), the solutions can be presented as:
\[
\text{Solution Set is } \{-9, \frac{3}{19}\}
\]
**Given the multiple choice answers you provided**, none match this exact solution. If you are looking for an approximate decimal value or a specific context for the answer, please let me know!