(x-3)(x+5)=-15

2 min read Jun 17, 2024

Solving the Equation (x - 3)(x + 5) = -15

This equation involves a quadratic expression and requires us to solve for the unknown variable 'x'. Let's break down the steps to find the solutions.

1. Expand the Left-Hand Side

First, we need to expand the left-hand side of the equation by using the distributive property (also known as FOIL):

(x - 3)(x + 5) = x² + 5x - 3x - 15

Simplifying this, we get:

x² + 2x - 15 = -15

2. Move all Terms to One Side

To solve a quadratic equation, we need to set it equal to zero. We can do this by adding 15 to both sides:

x² + 2x - 15 + 15 = -15 + 15

This gives us:

x² + 2x = 0

3. Factor the Quadratic Expression

Now, we can factor the left-hand side. The greatest common factor of x² and 2x is 'x'. Factoring out 'x', we get:

x(x + 2) = 0

4. Apply 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. Therefore, we have two possible solutions:

x = 0
x + 2 = 0

Solving for the second equation, we get:

x = -2

5. The Solutions

Therefore, the solutions to the equation (x - 3)(x + 5) = -15 are:

x = 0 and x = -2