Solving the Equation (x+5)(x+3) = 0
This equation represents a quadratic expression in factored form. Let's break down how to solve it and find the values of x that satisfy the equation.
Understanding the Zero Product Property
The key to solving this equation lies in the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.
In our equation, (x+5) and (x+3) are the two factors. For the product to be zero, either one or both of these factors must equal zero.
Finding the Solutions

Set the first factor to zero: x + 5 = 0 x = 5

Set the second factor to zero: x + 3 = 0 x = 3
Therefore, the solutions to the equation (x+5)(x+3) = 0 are x = 5 and x = 3.
Verifying the Solutions
We can verify our solutions by plugging them back into the original equation:

For x = 5: (5 + 5)(5 + 3) = (0)(2) = 0

For x = 3: (3 + 5)(3 + 3) = (2)(0) = 0
Both solutions satisfy the original equation, confirming that they are correct.
Conclusion
By applying the Zero Product Property, we were able to efficiently solve the quadratic equation (x+5)(x+3) = 0 and find the two solutions: x = 5 and x = 3. This method is a powerful tool for solving equations in factored form.