Solving the Equation (x+3)(x+4) = 0
This equation represents a quadratic equation in factored form. To find the solutions, we can use the Zero Product Property.
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.
Solving the Equation

Apply the Zero Product Property: Since the product of (x+3) and (x+4) equals zero, we know that either (x+3) = 0 or (x+4) = 0.

Solve for x in each equation:
 (x+3) = 0: Subtract 3 from both sides to get x = 3.
 (x+4) = 0: Subtract 4 from both sides to get x = 4.
Solutions
Therefore, the solutions to the equation (x+3)(x+4) = 0 are x = 3 and x = 4.
Verification
We can verify our solutions by substituting them back into the original equation:
 For x = 3: (3 + 3)(3 + 4) = (0)(1) = 0
 For x = 4: (4 + 3)(4 + 4) = (1)(0) = 0
Both solutions satisfy the original equation, confirming their validity.