Solving the Equation (x+4)(x^24x+16) = 0
This equation is already factored, making it relatively straightforward to solve. Here's how we can approach it:
Understanding the Equation
The equation represents the product of two factors:
 (x+4): This is a linear factor.
 (x^24x+16): This is a quadratic factor.
For the product of these factors to equal zero, at least one of the factors must be equal to zero.
Solving for x
Let's apply the zero product property:

Set each factor equal to zero:
 x + 4 = 0
 x^2  4x + 16 = 0

Solve the linear equation:
 x = 4

Solve the quadratic equation:

This quadratic equation doesn't factor easily, so we can use the quadratic formula:
 x = [b ± √(b^2  4ac)] / 2a
 Where a = 1, b = 4, and c = 16

Substituting the values:
 x = [4 ± √((4)^2  4 * 1 * 16)] / 2 * 1
 x = [4 ± √(48)] / 2
 x = [4 ± 4√(3)] / 2
 x = 2 ± 2√(3)
 x = 2 ± 2i√3 (where 'i' is the imaginary unit, √1)

Solutions
Therefore, the solutions to the equation (x+4)(x^24x+16) = 0 are:
 x = 4
 x = 2 + 2i√3
 x = 2  2i√3
The equation has one real solution (x = 4) and two complex solutions (x = 2 + 2i√3 and x = 2  2i√3).