(4k+5)(k+1)=0 Solve By Factoring

2 min read Jun 16, 2024

Solving the Equation (4k + 5)(k + 1) = 0 by Factoring

This equation is already factored for us, which makes solving it much easier. Let's break down the steps:

Understanding the Zero Product Property

The key to solving this equation is the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying the Zero Product Property

Identify the factors: In our equation, we have two factors: (4k + 5) and (k + 1).
Set each factor equal to zero:
- 4k + 5 = 0
- k + 1 = 0
Solve for k in each equation:
- 4k = -5
- k = -5/4
- k = -1

Solutions

Therefore, the solutions to the equation (4k + 5)(k + 1) = 0 are k = -5/4 and k = -1.

Verification

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

For k = -5/4:
- (4(-5/4) + 5)(-5/4 + 1) = (0)(-1/4) = 0
For k = -1:
- (4(-1) + 5)(-1 + 1) = (1)(0) = 0

Both solutions satisfy the original equation, confirming that our answers are correct.