(2x-5)(3x+2)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (2x-5)(3x+2) = 0

This equation represents a quadratic equation in factored form. To find the solutions for x, we can utilize 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.

Applying the Zero Product Property

1. Set each factor equal to zero:

   • 2x - 5 = 0
   • 3x + 2 = 0

2. Solve for x in each equation:

   • 2x - 5 = 0 => 2x = 5 => x = 5/2
   • 3x + 2 = 0 => 3x = -2 => x = -2/3

Solutions

Therefore, the solutions to the equation (2x-5)(3x+2) = 0 are:

• x = 5/2
• x = -2/3

These values of x are the roots of the quadratic equation, representing the points where the graph of the equation intersects the x-axis.