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

Jasonbradley

2 min read

·

Jun 16, 2024

14

Share

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

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can utilize 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, (2x + 1)(3x - 1) = 0, we have two factors: (2x + 1) and (3x - 1). Therefore, for the product to equal zero, at least one of these factors must be equal to zero.

Solving for x

1. Set the first factor equal to zero:

2x + 1 = 0

2x = -1

x = -1/2

2. Set the second factor equal to zero:

3x - 1 = 0

3x = 1

x = 1/3

Solutions

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

• x = -1/2
• x = 1/3

These solutions represent the points where the graph of the quadratic function intersects the x-axis.