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(x+3)(x-4)(x-6) 0

2 min read Jun 16, 2024
(x+3)(x-4)(x-6) 0

Solving the Equation (x+3)(x-4)(x-6) = 0

This equation involves a product of three factors that equals zero. This means at least one of the factors must be zero. We can solve this by setting each factor equal to zero and solving for x.

Steps to Solve:

  1. Set each factor equal to zero:

    • x + 3 = 0
    • x - 4 = 0
    • x - 6 = 0

  2. Solve each equation for x:

    • x = -3
    • x = 4
    • x = 6

Solution:

Therefore, the solutions to the equation (x+3)(x-4)(x-6) = 0 are x = -3, x = 4, and x = 6.

Understanding the Concept

This method is based on the Zero Product Property which states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In this example, the equation represents a cubic function, and the solutions we found are the x-intercepts of the function's graph. This means the graph of the function crosses the x-axis at the points (-3, 0), (4, 0), and (6, 0).

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