(2x-1)(x+3)=0 Quadratic Equation

2 min read Jun 16, 2024

Solving the Quadratic Equation (2x-1)(x+3) = 0

This article will guide you through solving the quadratic equation (2x-1)(x+3) = 0. We'll explore the concept of the Zero Product Property and apply it to find the solutions for 'x'.

Understanding the Zero Product Property

The Zero Product Property states that if the product of two or more factors equals zero, then at least one of the factors must be zero. This property is fundamental to solving equations in factored form.

Solving the Equation

Identify the Factors: Our equation is already factored: (2x-1)(x+3) = 0. We have two factors: (2x-1) and (x+3).
Apply the Zero Product Property: According to the property, either (2x-1) = 0 or (x+3) = 0.
Solve for 'x' in each factor:
- For (2x-1) = 0:
  - Add 1 to both sides: 2x = 1
  - Divide both sides by 2: x = 1/2
- For (x+3) = 0:
  - Subtract 3 from both sides: x = -3

Solutions

Therefore, the solutions to the quadratic equation (2x-1)(x+3) = 0 are:

x = 1/2
x = -3

Conclusion

By applying the Zero Product Property, we efficiently solved the quadratic equation (2x-1)(x+3) = 0 and found the two possible values for 'x'. This method is a simple and effective approach to solving quadratic equations that are already in factored form.