Solving the Quadratic Equation (m + 2)(m  5) = 0
This article will guide you through solving the quadratic equation (m + 2)(m  5) = 0. This equation is already factored, making the solution process quite straightforward.
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.
Applying the Zero Product Property

Identify the factors: In our equation, (m + 2) and (m  5) are the factors.

Set each factor equal to zero:
 m + 2 = 0
 m  5 = 0

Solve for 'm' in each equation:
 m = 2
 m = 5
The Solutions
Therefore, the solutions to the quadratic equation (m + 2)(m  5) = 0 are m = 2 and m = 5.
Verification
We can verify our solutions by substituting them back into the original equation:
 For m = 2: (2 + 2)(2  5) = (0)(7) = 0
 For m = 5: (5 + 2)(5  5) = (7)(0) = 0
Both solutions satisfy the original equation, confirming their validity.
Conclusion
Solving factored quadratic equations like (m + 2)(m  5) = 0 is a simple process thanks to the Zero Product Property. By setting each factor to zero and solving for the variable, we can quickly find the solutions. This method allows us to efficiently solve a wide range of quadratic equations.