(2m+3)(4m+3)=0 Solve By Factoring

3 min read Jun 16, 2024

Solving Quadratic Equations by Factoring: (2m+3)(4m+3)=0

This article will demonstrate how to solve the quadratic equation (2m+3)(4m+3)=0 using the factoring method.

Understanding the Problem

The given equation is already factored, presenting two expressions multiplied together that equal zero. This is a key concept in solving quadratic equations.

The Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero. This property is crucial in solving factored equations.

Solving for 'm'

Set each factor to zero:
- 2m + 3 = 0
- 4m + 3 = 0
Solve for 'm' in each equation:
- 2m = -3 m = -3/2
- 4m = -3 m = -3/4

The Solution

Therefore, the solutions to the equation (2m+3)(4m+3)=0 are:

m = -3/2
m = -3/4

Verification

To verify our solutions, we can substitute each value of 'm' back into the original equation:

For m = -3/2: (2(-3/2)+3)(4(-3/2)+3) = (0)(-3) = 0
For m = -3/4: (2(-3/4)+3)(4(-3/4)+3) = (3/2)(0) = 0

Since both substitutions result in zero, we have confirmed that our solutions are correct.

Conclusion

By applying the Zero Product Property and factoring, we successfully solved the quadratic equation (2m+3)(4m+3)=0, finding the solutions m = -3/2 and m = -3/4. This method demonstrates a simple and efficient way to solve quadratic equations that are already in factored form.