Solve the equation. \[ x^{2}-2 x-15=0 \]

To solve the equation \( x^{2}-2 x-15=0 \), we can factor it. We need two numbers that multiply to \(-15\) (the constant term) and add up to \(-2\) (the coefficient of \(x\)). These numbers are \(-5\) and \(3\). Thus, we can factor the equation as follows: \[ (x - 5)(x + 3) = 0 \] Setting each factor to zero gives us the solutions: 1. \( x - 5 = 0 \) → \( x = 5 \) 2. \( x + 3 = 0 \) → \( x = -3 \) Therefore, the solutions to the equation are \( x = 5 \) and \( x = -3 \).