(x+2)(x-1)=0

2 min read Jun 16, 2024

Solving the Equation (x+2)(x-1) = 0

The equation (x+2)(x-1) = 0 is a quadratic equation in factored form. Solving this equation involves finding the values of x that make the equation true.

The Zero Product Property

The key to solving this equation lies in the Zero Product Property. This 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 for x

Set each factor equal to zero:
- x + 2 = 0
- x - 1 = 0
Solve for x in each equation:
- x = -2
- x = 1

The Solution

Therefore, the solutions to the equation (x+2)(x-1) = 0 are x = -2 and x = 1. These values of x make the equation true because they cause one or both of the factors to equal zero, satisfying the Zero Product Property.

Verification

We can verify our solutions by substituting them back into the original equation:

For x = -2:
- (-2 + 2)(-2 - 1) = (0)(-3) = 0
For x = 1:
- (1 + 2)(1 - 1) = (3)(0) = 0

Since both solutions make the equation true, we have confirmed that our solutions are correct.