(4x-5)(x+3)=0

Jasonbradley

2 min read

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Jun 16, 2024

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Solving the Equation (4x - 5)(x + 3) = 0

This equation is already in a factored form, which makes it incredibly easy to solve. Let's break down the steps:

The Zero Product Property

The key to solving this equation lies in 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 our case, we have two factors:

• (4x - 5)
• (x + 3)

For the entire equation to equal zero, at least one of these factors must be zero.

Solving for x

Let's set each factor equal to zero and solve for x:

1. 4x - 5 = 0

• Add 5 to both sides: 4x = 5
• Divide both sides by 4: x = 5/4

2. x + 3 = 0

• Subtract 3 from both sides: x = -3

Solutions

Therefore, the solutions to the equation (4x - 5)(x + 3) = 0 are:

• x = 5/4
• x = -3

These are the values of x that make the equation true.