Solving the Equation (x+5)(x1) = 0
The equation (x+5)(x1) = 0 is a simple quadratic equation in factored form. This makes it incredibly easy to solve for the values of x that make the equation true.
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, we have two factors: (x+5) and (x1). For the product to be zero, either one or both of these factors must equal zero.
Solving for x
Therefore, we can set each factor equal to zero and solve for x:

x + 5 = 0 Subtracting 5 from both sides gives us: x = 5

x  1 = 0 Adding 1 to both sides gives us: x = 1
Solution
Therefore, the solutions to the equation (x+5)(x1) = 0 are x = 5 and x = 1. These values of x make the equation true.
Checking the Solution
We can check our solutions by substituting them back into the original equation:

For x = 5: (5 + 5)(5  1) = (0)(6) = 0. The equation holds true.

For x = 1: (1 + 5)(1  1) = (6)(0) = 0. The equation holds true.
This confirms that our solutions are correct.