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

2 min read Jun 17, 2024

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

This article will guide you through the steps of solving the equation (x-1)(x+2) = -2. We'll break down the process and explain each step clearly.

Step 1: Expanding the Left Side

First, we need to expand the left side of the equation by multiplying the two binomials:

(x-1)(x+2) = x² + 2x - x - 2

Simplifying this, we get:

x² + x - 2 = -2

Step 2: Moving All Terms to One Side

Next, we want to set the equation equal to zero. To do this, we'll add 2 to both sides:

x² + x - 2 + 2 = -2 + 2

This simplifies to:

x² + x = 0

Step 3: Factoring the Equation

Now we need to factor the quadratic expression on the left side. Notice that both terms have a common factor of 'x':

x(x + 1) = 0

Step 4: Applying the Zero Product Property

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x:

x = 0 or x + 1 = 0

Solving the second equation, we get:

x = -1

Step 5: Solutions

Therefore, the solutions to the equation (x-1)(x+2) = -2 are:

x = 0 x = -1