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Solving the Equation (x+4)(x-3) = 0
This equation represents a simple quadratic equation in factored form. Let's break down how to solve it:
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+4) and (x-3) are the two factors. Therefore, for the entire product to equal zero, one or both of these factors must equal zero.
Solving for x
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Set each factor equal to zero:
- x + 4 = 0
- x - 3 = 0
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Solve for x in each equation:
- x = -4
- x = 3
The Solutions
Therefore, the solutions to the equation (x+4)(x-3) = 0 are x = -4 and x = 3.
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = -4:
- (-4 + 4)(-4 - 3) = (0)(-7) = 0
- For x = 3:
- (3 + 4)(3 - 3) = (7)(0) = 0
Both solutions satisfy the original equation, confirming their validity.
Conclusion
Solving equations in factored form is a straightforward process that relies on the Zero Product Property. By setting each factor equal to zero and solving for the variable, we can efficiently find the solutions to the equation.