(x+2)(x-3)=0

2 min read Jun 16, 2024

Solving the Equation (x+2)(x-3) = 0

This equation represents a simple quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can utilize the Zero Product Property.

The 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.

In our equation, (x+2)(x-3) = 0, we have two factors: (x+2) and (x-3). Therefore, for the product to be zero, either:

(x + 2) = 0
(x - 3) = 0

Solving for x

Let's solve each equation separately:

(x + 2) = 0
- Subtracting 2 from both sides, we get: x = -2
(x - 3) = 0
- Adding 3 to both sides, we get: x = 3

Solutions

Therefore, the solutions to the equation (x+2)(x-3) = 0 are x = -2 and x = 3. These values are the roots of the quadratic equation.

Visual Representation

The equation represents a parabola that intersects the x-axis at the points (-2, 0) and (3, 0). These points correspond to the solutions we found.

Conclusion

By applying the Zero Product Property, we effectively solved the equation (x+2)(x-3) = 0, finding the two distinct roots x = -2 and x = 3. This approach provides a straightforward method for solving factored quadratic equations.