(3n-2)(4n+1)=0 Solve By Factoring

2 min read Jun 16, 2024

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

This equation is already in factored form, making it easy to solve. Here's how:

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 other words:

If a * b = 0, then either a = 0 or b = 0 (or both).

Applying the Zero Product Property

Identify the factors: In our equation (3n - 2)(4n + 1) = 0, we have two factors: (3n - 2) and (4n + 1).
Set each factor equal to zero:
- 3n - 2 = 0
- 4n + 1 = 0
Solve for 'n' in each equation:
- For 3n - 2 = 0:
  - Add 2 to both sides: 3n = 2
  - Divide both sides by 3: n = 2/3
- For 4n + 1 = 0:
  - Subtract 1 from both sides: 4n = -1
  - Divide both sides by 4: n = -1/4

Solutions

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