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(x+3)(x+2)=0

2 min read Jun 16, 2024
(x+3)(x+2)=0

Solving the Equation (x+3)(x+2) = 0

This equation is a simple quadratic equation, and we can solve it using 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.

Here's how to solve the equation:

  1. Set each factor equal to zero:

    • x + 3 = 0
    • x + 2 = 0

  2. Solve for x in each equation:

    • x = -3
    • x = -2

Therefore, the solutions to the equation (x+3)(x+2) = 0 are x = -3 and x = -2.

Understanding the Zero Product Property

The Zero Product Property is a fundamental concept in algebra. It allows us to break down complex equations into simpler ones. In this case, we can see that the equation is true if either (x+3) or (x+2) is equal to zero. This makes it much easier to find the solutions.

Visualizing the Solution

We can also visualize the solution graphically. The equation (x+3)(x+2) = 0 represents a parabola that intersects the x-axis at the points (-3, 0) and (-2, 0). These points correspond to the solutions we found using the Zero Product Property.

Conclusion

Solving the equation (x+3)(x+2) = 0 is a straightforward process that illustrates the importance of the Zero Product Property. Understanding this property is crucial for solving a wide range of algebraic equations.

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