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Solving the Equation (n+2)(2n+5)=0
This article will guide you through solving the equation (n+2)(2n+5)=0.
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: (n+2) and (2n+5). To make the product equal to zero, one or both of these factors must be equal to zero.
Solving for n
Let's set each factor equal to zero and solve for n:
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n + 2 = 0 Subtracting 2 from both sides, we get: n = -2
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2n + 5 = 0 Subtracting 5 from both sides, we get: 2n = -5 Dividing both sides by 2, we get: n = -5/2
Conclusion
Therefore, the solutions to the equation (n+2)(2n+5)=0 are n = -2 and n = -5/2. These values of n make the equation true.