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

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

### Understanding 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) is a factor that appears twice.

### Solving for x

To find the solutions, we apply the Zero Product Property:

**Set each factor equal to zero:**- (x-6) = 0

**Solve for x:**- x = 6

### The Solution

Therefore, the solution to the equation (x-6)(x-6) = 0 is **x = 6**. This solution has a **multiplicity of 2**, meaning it appears twice in the factored form of the equation.

### Visualizing the Solution

Graphically, this equation represents a parabola that intersects the x-axis at the point x = 6. The fact that the solution has a multiplicity of 2 indicates that the parabola touches the x-axis at this point, but doesn't cross it.

### Conclusion

Solving the equation (x-6)(x-6) = 0 involves utilizing the Zero Product Property, which leads to a single solution, x = 6, with a multiplicity of 2. Understanding the Zero Product Property is essential for solving factored quadratic equations.