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Solving the Equation (x+10)(x-3) = 0
This equation is a simple quadratic equation in factored form. Let's break down how to solve it.
Understanding 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.
In our equation, (x+10) and (x-3) are the factors.
Solving for x
To solve for x, we set each factor equal to zero and solve the resulting equations:
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Factor 1: x + 10 = 0 Subtracting 10 from both sides, we get: x = -10
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Factor 2: x - 3 = 0 Adding 3 to both sides, we get: x = 3
Solutions
Therefore, the solutions to the equation (x+10)(x-3) = 0 are x = -10 and x = 3.
Verification
We can verify our solutions by substituting each value of x back into the original equation:
- For x = -10: (-10 + 10)(-10 - 3) = (0)(-13) = 0
- For x = 3: (3 + 10)(3 - 3) = (13)(0) = 0
Since both substitutions result in 0, we have confirmed that our solutions are correct.