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(x^2-x-6)*(x+4)=0

2 min read Jun 17, 2024
(x^2-x-6)*(x+4)=0

Solving the Equation (x^2 - x - 6)(x + 4) = 0

This equation is a polynomial equation of degree three. To solve it, we can use 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.

Step 1: Factor the quadratic expression

The quadratic expression (x² - x - 6) can be factored as (x - 3)(x + 2).

Step 2: Apply the Zero Product Property

Now, the equation becomes:

(x - 3)(x + 2)(x + 4) = 0

For this product to be zero, one or more of the factors must be zero. So, we set each factor equal to zero and solve for x:

  • x - 3 = 0 => x = 3
  • x + 2 = 0 => x = -2
  • x + 4 = 0 => x = -4

Therefore, the solutions to the equation (x² - x - 6)(x + 4) = 0 are x = 3, x = -2, and x = -4.

In summary:

  • We factored the quadratic expression.
  • We applied the Zero Product Property to set each factor equal to zero.
  • We solved for x in each equation.

This method provides us with all the solutions to the given equation.

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