(3x%2B4)%3D0.jpeg "(x+1)(3x+4)=0")
Solving the Equation (x + 1)(3x + 4) = 0
This equation is a quadratic equation in factored form. To solve it, we can utilize the Zero Product Property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero.
Step 1: Set each factor equal to zero:
- x + 1 = 0
- 3x + 4 = 0
Step 2: Solve each equation for x:
- x = -1
- x = -4/3
Therefore, the solutions to the equation (x + 1)(3x + 4) = 0 are x = -1 and x = -4/3.
Explanation:
This equation represents a parabola that intersects the x-axis at two points. The x-coordinates of these points are the solutions we found. In other words, plugging in either x = -1 or x = -4/3 into the original equation will make the equation true.
Important Note:
The Zero Product Property is a powerful tool for solving quadratic equations in factored form. By setting each factor equal to zero, we can quickly and easily find the solutions.