(x+3) (x+4)=0 Quadratic Equation

2 min read Jun 16, 2024

Solving the Quadratic Equation (x+3)(x+4) = 0

This article will guide you through solving the quadratic equation (x+3)(x+4) = 0.

Understanding the Equation

The equation is already factored, which makes solving it much easier. We have two factors multiplied together, resulting in zero. This means that at least one of these factors must be equal to zero.

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.

Solving the Equation

Set each factor equal to zero:
- x + 3 = 0
- x + 4 = 0
Solve for x in each equation:
- x = -3
- x = -4

The Solution

Therefore, the solutions to the quadratic equation (x+3)(x+4) = 0 are x = -3 and x = -4. These are the values of x that make the equation true.

Verification

We can verify our solution by plugging each value of x back into the original equation:

For x = -3:
- (-3 + 3)(-3 + 4) = (0)(1) = 0
For x = -4:
- (-4 + 3)(-4 + 4) = (-1)(0) = 0

Since both values of x satisfy the original equation, we have confirmed our solution.