Solving the Equation (x+2)(x+9)=0
This equation represents a quadratic equation 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, we have two factors: (x+2) and (x+9). For the product of these factors to be zero, either (x+2) must equal zero or (x+9) must equal zero.
Solving for x
Let's set each factor equal to zero and solve for x:

For (x+2) = 0:
 Subtract 2 from both sides: x = 2

For (x+9) = 0:
 Subtract 9 from both sides: x = 9
Solution
Therefore, the solutions to the equation (x+2)(x+9)=0 are x = 2 and x = 9.
These values of x make the equation true because when substituted into the original equation, they result in a product of zero.