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

Jasonbradley

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Jun 16, 2024

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

This equation is a quadratic equation in disguise, but it's much easier to solve than a standard quadratic. Let's break down how to find the solutions:

Understanding the Zero Product Property

The equation (3n-2)(4n+1) = 0 relies on the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In other words, if a * b = 0, then either a = 0 or b = 0 (or both).

Applying the Zero Product Property

1. Set each factor equal to zero:

   • 3n - 2 = 0
   • 4n + 1 = 0

2. Solve for 'n' in each equation:

   • 3n = 2
     • n = 2/3
   • 4n = -1
     • n = -1/4

The Solutions

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

• n = 2/3
• n = -1/4

These are the values of 'n' that make the entire equation true.