(3n+2)(n-2)=0

2 min read Jun 16, 2024

Solving the Quadratic Equation: (3n + 2)(n - 2) = 0

This article explores the solution process for the quadratic equation (3n + 2)(n - 2) = 0.

Understanding the Zero Product Property

The equation is already factored, which makes it easier to solve. 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.

Solving for n

Applying the Zero Product Property to our equation, we get:

3n + 2 = 0
n - 2 = 0

Solving for n in each equation:

3n = -2
n = -2/3
n = 2

Conclusion

Therefore, the solutions to the quadratic equation (3n + 2)(n - 2) = 0 are n = -2/3 and n = 2. These are the values of n that make the equation true.

Note:

This method relies on the equation already being factored. If the equation is not factored, you would need to use techniques like factoring, completing the square, or the quadratic formula to solve for n.