(x-6)(x+4)=0

2 min read Jun 17, 2024

Solving the Equation (x-6)(x+4) = 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) and (x+4) are the factors. Therefore, to find the solutions, we need to set each factor equal to zero:

x - 6 = 0
x + 4 = 0

Solving for x

Now, we solve each equation for x:

x = 6
x = -4

Solutions

Therefore, the solutions to the equation (x-6)(x+4) = 0 are x = 6 and x = -4.

Interpretation

These solutions represent the points where the graph of the quadratic function y = (x-6)(x+4) intersects the x-axis. This is because when y = 0, the function crosses the x-axis.

Conclusion

By applying the Zero Product Property, we can easily solve factored quadratic equations like (x-6)(x+4) = 0. This method provides us with the two distinct solutions: x = 6 and x = -4.