To solve the factored quadratic equation \((x−5)(x+3)=0\), we set each factor equal to zero:
-
\(x - 5 = 0\)
Solving for \(x\) gives: \[ x = 5 \] -
\(x + 3 = 0\)
Solving for \(x\) gives: \[ x = -3 \]
Thus, the solutions are \(x = -3\) and \(x = 5\).
The smaller solution is \(x = -3\), and the larger solution is \(x = 5\).