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

2 min read Jun 17, 2024
(x-3)(x+2)=0

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

This equation is a simple quadratic equation that can be solved 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.

Let's break down the solution:

  1. Identify the Factors: The equation is already factored for us: (x-3)(x+2) = 0. We have two factors: (x-3) and (x+2).

  2. Apply the Zero Product Property: Since the product of these factors is zero, we know that at least one of them must be equal to zero.

  3. Set each factor equal to zero:

    • x - 3 = 0
    • x + 2 = 0

  4. Solve for x:

    • x = 3
    • x = -2

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

Verification:

We can verify our solutions by plugging them back into the original equation:

  • For x = 3: (3-3)(3+2) = 0 * 5 = 0. This confirms that x = 3 is a valid solution.

  • For x = -2: (-2-3)(-2+2) = -5 * 0 = 0. This confirms that x = -2 is also a valid solution.

Conclusion:

The equation (x-3)(x+2) = 0 has two solutions: x = 3 and x = -2. This demonstrates the power of factoring and the Zero Product Property in solving quadratic equations.

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