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(x+7)(x+5)=0

2 min read Jun 17, 2024
(x+7)(x+5)=0

Solving the Equation (x+7)(x+5) = 0

This equation is a simple quadratic equation in factored form. 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.

Let's break down the steps:

  1. Identify the factors: The equation is already factored for us: (x+7)(x+5) = 0. We have two factors: (x+7) and (x+5).

  2. Apply the Zero Product Property: For the product of the factors to be zero, at least one of them must be zero. Therefore, we have two possible scenarios:

    • x + 7 = 0
    • x + 5 = 0

  3. Solve for x in each scenario:

    • x + 7 = 0 => x = -7
    • x + 5 = 0 => x = -5

  4. Solutions: The solutions to the equation (x+7)(x+5) = 0 are x = -7 and x = -5.

In conclusion, the equation (x+7)(x+5) = 0 has two solutions, x = -7 and x = -5. This demonstrates how the Zero Product Property can simplify solving factored quadratic equations.

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