(x-6)(x+2)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-6)(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.

Here's how to solve it:

1. Set each factor equal to zero:

   • x - 6 = 0
   • x + 2 = 0

2. Solve for x in each equation:

   • x = 6
   • x = -2

Therefore, the solutions to the equation (x-6)(x+2) = 0 are x = 6 and x = -2.

Explanation:

When we substitute x = 6 or x = -2 into the original equation, the equation becomes true because one of the factors becomes zero, making the entire product equal to zero.

Visualizing the Solution:

We can also visualize the solution by graphing the equation y = (x-6)(x+2). The graph will intersect the x-axis at x = 6 and x = -2, which represent the solutions to the equation.

In conclusion, solving the equation (x-6)(x+2) = 0 is straightforward using the Zero Product Property. We obtain two solutions, x = 6 and x = -2, which can be visualized as the x-intercepts of the graph of the equation.