(x+3)(x+8)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x+3)(x+8) = 0

This equation is a simple quadratic equation in factored form. Let's break down how to solve it.

Understanding the Zero Product Property

The core principle behind solving this equation is 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.

Applying the Zero Product Property

1. Identify the factors: In our equation, (x+3) and (x+8) are the factors.
2. Set each factor equal to zero:
   • x + 3 = 0
   • x + 8 = 0
3. Solve for x in each equation:
   • x = -3
   • x = -8

Solution

Therefore, the solutions to the equation (x+3)(x+8) = 0 are x = -3 and x = -8.

Verification

We can verify these solutions by plugging them back into the original equation:

• For x = -3: (-3 + 3)(-3 + 8) = (0)(5) = 0
• For x = -8: (-8 + 3)(-8 + 8) = (-5)(0) = 0

Since both solutions result in 0 when substituted back into the equation, we have confirmed that they are indeed the correct solutions.