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Solving the Equation (x+4)(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 use the Zero Product Property.
The Zero Product Property
The Zero Product 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+5) are the two factors. Therefore, for the product to be zero, at least one of these factors must be zero.
Solving for x
We can set each factor equal to zero and solve for x:
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x + 4 = 0 Subtracting 4 from both sides gives us: x = -4
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x + 5 = 0 Subtracting 5 from both sides gives us: x = -5
Solution
Therefore, the solutions to the equation (x+4)(x+5) = 0 are x = -4 and x = -5.
These values of x are the roots of the equation, which are the points where the graph of the equation intersects the x-axis.