Solving the Equation (x+4)(x5) = 0
This equation represents a quadratic equation in factored form. To solve for the values of x, we can use the Zero Product Property.
The Zero Product Property
This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero. In our equation:
(x + 4)(x  5) = 0
We have two factors: (x + 4) and (x  5). To make the product equal to zero, at least one of these factors must be zero.
Solving for x
Therefore, we set each factor equal to zero and solve:

x + 4 = 0 Subtracting 4 from both sides, we get: x = 4

x  5 = 0 Adding 5 to both sides, we get: x = 5
The Solutions
Therefore, the solutions to the equation (x + 4)(x  5) = 0 are x = 4 and x = 5.
Checking the Solutions
We can verify our solutions by plugging them back into the original equation:

For x = 4: (4 + 4)(4  5) = (0)(9) = 0

For x = 5: (5 + 4)(5  5) = (9)(0) = 0
Both solutions satisfy the original equation, confirming our results.