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(2x-1)(3x+4)=0

2 min read Jun 16, 2024
(2x-1)(3x+4)=0

Solving the Equation (2x-1)(3x+4) = 0

This equation represents a 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, we have two factors: (2x - 1) and (3x + 4). The equation tells us that their product equals zero. Therefore, at least one of these factors must be equal to zero.

Finding the Solutions

We now have two simple equations to solve:

  1. 2x - 1 = 0

    • Add 1 to both sides: 2x = 1
    • Divide both sides by 2: x = 1/2

  2. 3x + 4 = 0

    • Subtract 4 from both sides: 3x = -4
    • Divide both sides by 3: x = -4/3

The Solutions

Therefore, the solutions to the equation (2x - 1)(3x + 4) = 0 are:

x = 1/2 and x = -4/3

These values are the points where the graph of the quadratic function represented by the equation intersects the x-axis.

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