Solving the Equation (a  3)(a + 4) = 0
This equation presents a straightforward example of solving quadratic equations using 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.
Understanding the Zero Product Property
In our equation, (a  3) and (a + 4) are the two factors. To make the product equal to zero, either:
 (a  3) = 0
 (a + 4) = 0
Solving for 'a'
Let's solve each equation individually:

(a  3) = 0 Adding 3 to both sides, we get: a = 3

(a + 4) = 0 Subtracting 4 from both sides, we get: a = 4
Solution
Therefore, the solutions to the equation (a  3)(a + 4) = 0 are:
 a = 3
 a = 4
These values of 'a' will make the equation true because they cause one of the factors to be zero, resulting in the product of the factors being zero.