Solving the Equation (x+3)(x4)(2x+1) = 0
This equation is a cubic equation, meaning it has a highest power of x of 3. To solve it, we can use the Zero Product Property:
Zero Product Property
If the product of several factors is zero, then at least one of the factors must be zero.
Applying the Zero Product Property
In our equation, we have three factors:
 (x+3)
 (x4)
 (2x+1)
To make the product equal to zero, at least one of these factors must be zero. So, we set each factor equal to zero and solve for x:

x + 3 = 0
 x = 3

x  4 = 0
 x = 4

2x + 1 = 0
 2x = 1
 x = 1/2
Solutions
Therefore, the solutions to the equation (x+3)(x4)(2x+1) = 0 are:
 x = 3
 x = 4
 x = 1/2
Graphing the Equation
The graph of this equation will intersect the xaxis at these three points, representing the solutions:
 (3, 0)
 (4, 0)
 (1/2, 0)