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

Jasonbradley

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Jun 16, 2024

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

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can utilize the Zero Product Property.

The Zero Product Property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Let's apply this to our equation:

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

This means either:

• 3x - 2 = 0
• x + 5 = 0

Now we solve each equation separately:

For 3x - 2 = 0:

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

For x + 5 = 0:

1. Subtract 5 from both sides: x = -5

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

These solutions represent the x-intercepts of the quadratic function represented by the equation.