(2x-1)(x+3)=0

Jasonbradley

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Jun 16, 2024

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

This equation is a quadratic equation in factored form. Let's break down how to solve it:

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. This property is the key to solving our equation.

Solving the Equation

1. Set each factor equal to zero:

   • 2x - 1 = 0
   • x + 3 = 0

2. Solve for x in each equation:

   • 2x = 1

   • x = 1/2

   • x = -3

Solutions

Therefore, the solutions to the equation (2x-1)(x+3) = 0 are x = 1/2 and x = -3.

Verification

We can verify our solutions by substituting them back into the original equation:

• For x = 1/2:

  • (2(1/2) - 1)(1/2 + 3) = (1 - 1)(7/2) = 0 * (7/2) = 0

• For x = -3:

  • (2(-3) - 1)(-3 + 3) = (-7)(0) = 0

Since both substitutions result in a true statement (0 = 0), we have confirmed that our solutions are correct.