(x-6)(x+3) 0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-6)(x+3) = 0

This equation represents a quadratic expression set equal to zero. To solve for the values of x that satisfy the equation, we can utilize 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 steps:

1. Identify the factors: The equation is already factored into two factors: (x-6) and (x+3).
2. Apply the Zero Product Property: We know that the product of these two factors is equal to zero. Therefore, at least one of these factors must be zero.
3. Set each factor equal to zero:
   • x - 6 = 0
   • x + 3 = 0
4. Solve for x:
   • x = 6
   • x = -3

Therefore, the solutions to the equation (x-6)(x+3) = 0 are x = 6 and x = -3.

Understanding the Solution

These solutions represent the x-intercepts of the parabola defined by the quadratic equation. This means that the graph of the equation will cross the x-axis at the points (6, 0) and (-3, 0).

In summary, the equation (x-6)(x+3) = 0 is solved by utilizing the Zero Product Property, which leads to the solutions x = 6 and x = -3.