(x+6)(x-1) 0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x+6)(x-1) = 0

This equation represents a quadratic expression in factored form. To find the solutions (or roots) of this equation, we can use the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Applying the Zero Product Property:

1. Set each factor equal to zero:

   • x + 6 = 0
   • x - 1 = 0

2. Solve for x in each equation:

   • x = -6
   • x = 1

Therefore, the solutions to the equation (x+6)(x-1) = 0 are x = -6 and x = 1.

Explanation:

This means that if we substitute either -6 or 1 for x in the original equation, the entire expression will equal zero.

Visualizing the Solution:

The equation (x+6)(x-1) = 0 represents a parabola that intersects the x-axis at two points: x = -6 and x = 1. These points of intersection are the solutions to the equation.

In Summary:

The Zero Product Property is a powerful tool for solving equations in factored form. By setting each factor equal to zero and solving, we can easily determine the solutions to the equation.