(4m%2B3)%3D0.jpeg "(2m+3)(4m+3)=0")
Solving the Equation (2m + 3)(4m + 3) = 0
This equation represents a quadratic equation in factored form. To solve for m, we can utilize 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.
Here's how to solve the equation:
-
Set each factor equal to zero:
- 2m + 3 = 0
- 4m + 3 = 0
-
Solve for m in each equation:
-
For 2m + 3 = 0:
- Subtract 3 from both sides: 2m = -3
- Divide both sides by 2: m = -3/2
-
For 4m + 3 = 0:
- Subtract 3 from both sides: 4m = -3
- Divide both sides by 4: m = -3/4
-
Therefore, the solutions to the equation (2m + 3)(4m + 3) = 0 are m = -3/2 and m = -3/4.
Understanding the Zero Product Property
The Zero Product Property is a fundamental concept in algebra. It allows us to solve equations by breaking them down into simpler factors. In this case, we were able to easily find the solutions for m by setting each factor equal to zero.
Visual Representation
The solutions to this equation represent the x-intercepts of the quadratic function represented by the equation. This means that the graph of the function would cross the x-axis at the points x = -3/2 and x = -3/4.