Solving the Cubic Equation: (x+4)(x7)(x+8) = 0
This equation represents a cubic polynomial set equal to zero. To find the solutions (also known as roots or zeros), we can use the Zero Product Property. This property states that if the product of several factors is zero, at least one of the factors must be zero.
Let's break down the equation and apply this property:
(x+4)(x7)(x+8) = 0
This equation tells us that the product of three factors is zero. Therefore, at least one of these factors must be zero. This gives us three possible scenarios:
 x + 4 = 0
 x  7 = 0
 x + 8 = 0
Now, we simply solve each of these linear equations to find the values of x:

x + 4 = 0
 Subtract 4 from both sides: x = 4

x  7 = 0
 Add 7 to both sides: x = 7

x + 8 = 0
 Subtract 8 from both sides: x = 8
Therefore, the solutions to the equation (x+4)(x7)(x+8) = 0 are x = 4, x = 7, and x = 8.
In conclusion, the equation has three distinct real roots: 4, 7, and 8.