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(x-6)(x+7)=0

2 min read Jun 17, 2024
(x-6)(x+7)=0

Solving the Equation (x-6)(x+7) = 0

This equation represents a simple quadratic equation in factored form. To find the solutions for x, we can utilize 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.

Applying the Zero Product Property:

  1. Set each factor equal to zero:

    • (x - 6) = 0
    • (x + 7) = 0

  2. Solve for x in each equation:

    • x - 6 = 0 => x = 6
    • x + 7 = 0 => x = -7

Therefore, the solutions to the equation (x - 6)(x + 7) = 0 are x = 6 and x = -7.

Explanation:

  • The equation represents a parabola that intersects the x-axis at two points: x = 6 and x = -7.
  • These points are the roots or solutions to the equation, indicating where the value of the expression is equal to zero.

In summary, by applying the Zero Product Property, we effectively isolate the values of x that make the equation true, leading to the solutions x = 6 and x = -7.

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