(x-1)(x+5) 0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-1)(x+5) = 0

This equation is a simple 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

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.

Applying the Property

In our equation, (x-1)(x+5) = 0, we have two factors: (x-1) and (x+5). Therefore, to satisfy the equation, at least one of these factors must equal zero.

• Case 1: (x-1) = 0

  • Solving for x, we get x = 1.

• Case 2: (x+5) = 0

  • Solving for x, we get x = -5.

Solution

Therefore, the solutions to the equation (x-1)(x+5) = 0 are x = 1 and x = -5.

Verification

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

• For x = 1: (1-1)(1+5) = (0)(6) = 0
• For x = -5: (-5-1)(-5+5) = (-6)(0) = 0

Both solutions satisfy the equation, confirming our results.