What values of \( a \) satisfy the equation \( (a - 5)(a + 1) = 0 \)?

To solve the equation \( (a - 5)(a + 1) = 0 \), we can use the zero product property, which states that if the product of two factors is zero, at least one of the factors must be zero. Setting each factor equal to zero gives us two equations to solve: 1. \( a - 5 = 0 \) 2. \( a + 1 = 0 \) Solving the first equation: - \( a - 5 = 0 \) - Adding 5 to both sides, we find \( a = 5 \). Solving the second equation: - \( a + 1 = 0 \) - Subtracting 1 from both sides, we find \( a = -1 \). Therefore, the values of \( a \) that satisfy the equation \( (a - 5)(a + 1) = 0 \) are \( a = 5 \) and \( a = -1 \).