(x-3)(x-7)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-3)(x-7) = 0

This equation is a simple quadratic equation that can be solved using the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Let's break down the solution:

1. Identify the factors: The equation (x-3)(x-7) = 0 has two factors: (x-3) and (x-7).

2. Apply the Zero Product Property: For the product of these factors to be zero, either (x-3) = 0 or (x-7) = 0.

3. Solve for x:

   • For (x-3) = 0, we add 3 to both sides to get x = 3.
   • For (x-7) = 0, we add 7 to both sides to get x = 7.

Therefore, the solutions to the equation (x-3)(x-7) = 0 are x = 3 and x = 7.

In summary:

• We used the Zero Product Property to solve the equation.
• The solutions are the values of x that make each factor equal to zero.
• The solutions to the equation are x = 3 and x = 7.