(x-6)(x-3)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-6)(x-3) = 0

This equation represents a simple quadratic equation in factored form. To solve for the values of 'x' that satisfy this equation, we can use the Zero Product Property.

The Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In our equation, (x-6) and (x-3) are the two factors. So, according to the Zero Product Property, we have two possibilities:

1. x - 6 = 0 Solving for x, we get x = 6.

2. x - 3 = 0 Solving for x, we get x = 3.

Solution

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

Verification

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

• For x = 6: (6 - 6)(6 - 3) = 0 * 3 = 0
• For x = 3: (3 - 6)(3 - 3) = -3 * 0 = 0

Since both solutions result in 0, we have confirmed that they are indeed the correct solutions.