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

less than a minute read Jun 16, 2024
(3x-2)(x+4)=0

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

This equation is in a factored form, which makes solving for x much simpler. Here's how to approach it:

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, (3x - 2) and (x + 4) are the two factors. Therefore, for the entire equation to equal zero, either:

  • 3x - 2 = 0
  • x + 4 = 0

Solving for x

Now, we solve each equation individually:

1. 3x - 2 = 0

  • Add 2 to both sides: 3x = 2
  • Divide both sides by 3: x = 2/3

2. x + 4 = 0

  • Subtract 4 from both sides: x = -4

The Solutions

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

  • x = 2/3
  • x = -4

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