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**. This property states that if the product of two factors is zero, then at least one of the factors must be zero. Here's how to apply it step by step: 1. **Set Each Factor Equal to Zero:** \[ a - 5 = 0 \quad \text{or} \quad a + 1 = 0 \] 2. **Solve Each Equation Individually:** - For \( a - 5 = 0 \): \[ a = 5 \] - For \( a + 1 = 0 \): \[ a = -1 \] 3. **Combine the Solutions:** The values of \( a \) that satisfy the original equation are: \[ a = 5 \quad \text{and} \quad a = -1 \] **Conclusion:** The equation \( (a - 5)(a + 1) = 0 \) is satisfied when \( a = 5 \) or \( a = -1 \).