(2x+3)(3x-7)=0 Zero Product Property

Jasonbradley

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Jun 16, 2024

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Solving Equations using 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. This property is extremely useful when solving equations that are factored.

Let's take the equation (2x + 3)(3x - 7) = 0 as an example.

1. Identify the factors:

The equation is already factored, with (2x + 3) and (3x - 7) being the two factors.

2. Apply the Zero Product Property:

According to the Zero Product Property, either (2x + 3) = 0 or (3x - 7) = 0.

3. Solve for x:

• For (2x + 3) = 0:
  • Subtract 3 from both sides: 2x = -3
  • Divide both sides by 2: x = -3/2
• For (3x - 7) = 0:
  • Add 7 to both sides: 3x = 7
  • Divide both sides by 3: x = 7/3

4. The Solutions:

Therefore, the solutions to the equation (2x + 3)(3x - 7) = 0 are x = -3/2 and x = 7/3.

Key points:

• The Zero Product Property simplifies solving factored equations.
• It allows us to break down a complex equation into simpler linear equations.
• The solutions are the values of x that make the original equation true.

By understanding and applying the Zero Product Property, you can efficiently solve equations that are expressed in factored form.