Solving the Quadratic Equation: (x+3)(x5) = 0
This article will guide you through solving the quadratic equation (x+3)(x5) = 0. We'll explore the concepts behind this type of equation and break down the steps for finding its solutions.
Understanding the Equation
The equation (x+3)(x5) = 0 represents a quadratic equation in factored form. Here's why:
 Quadratic Equation: A quadratic equation is an equation of the form ax² + bx + c = 0, where 'a', 'b', and 'c' are constants and 'a' is not equal to 0.
 Factored Form: When a quadratic equation is written as a product of two linear expressions, like (x+3)(x5), it's in factored form.
The Zero Product Property
The key to solving this equation lies in the Zero Product Property. This property states:
 If the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.
Applying this to our equation:
 If (x+3)(x5) = 0, then either (x+3) = 0 or (x5) = 0 (or both).
Solving for x
Now, we can solve each of the linear equations:

x + 3 = 0
 Subtract 3 from both sides: x = 3

x  5 = 0
 Add 5 to both sides: x = 5
The Solutions
Therefore, the solutions to the quadratic equation (x+3)(x5) = 0 are:
 x = 3
 x = 5
These solutions represent the xintercepts of the parabola represented by the quadratic equation.
In Summary
By utilizing the Zero Product Property, we successfully solved the quadratic equation (x+3)(x5) = 0, finding two distinct solutions: x = 3 and x = 5. This process highlights the importance of recognizing factored forms of quadratic equations and how they simplify the solution process.