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Solving the Equation (x-7)(x+5) = 0
This equation represents a quadratic expression in factored form. Let's break down how to solve for the values of 'x' that satisfy this equation.
Understanding the Zero Product Property
The key to solving this equation lies in 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.
In our equation, (x-7) and (x+5) are the two factors. Therefore, to make the product equal to zero, at least one of these factors must be equal to zero.
Solving for x
We have two possibilities:
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x - 7 = 0 Adding 7 to both sides, we get: x = 7
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x + 5 = 0 Subtracting 5 from both sides, we get: x = -5
Conclusion
Therefore, the solutions to the equation (x-7)(x+5) = 0 are x = 7 and x = -5. These values of 'x' make the equation true.