(x+3)(x+2)=0 Standard Form

3 min read Jun 16, 2024

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

The equation (x+3)(x+2) = 0 is already in a factored form. This form makes it easy to solve for the values of x that satisfy the equation.

Understanding 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.

In our case, we have two factors: (x+3) and (x+2). For the product to be zero, either (x+3) = 0 or (x+2) = 0.

Solving for x

Let's solve for x in each case:

Case 1: (x+3) = 0 Subtracting 3 from both sides, we get x = -3.
Case 2: (x+2) = 0 Subtracting 2 from both sides, we get x = -2.

Solutions

Therefore, the solutions to the equation (x+3)(x+2) = 0 are x = -3 and x = -2.

Standard Form

While the equation is already in a factored form, we can also express it in the standard form of a quadratic equation:

ax² + bx + c = 0

To do this, we need to expand the factored form:

(x+3)(x+2) = x² + 2x + 3x + 6 = x² + 5x + 6 = 0

This is the standard form of the equation.

In conclusion, the solutions to the equation (x+3)(x+2) = 0 are x = -3 and x = -2. The equation in standard form is x² + 5x + 6 = 0.