(X)(x+2)(x-(2+i))=0

Solution for (X)(x+2)(x-(2+i))=0 equation:

Simplifying
(X)(x + 2)(x + -1(2 + i)) = 0

Reorder the terms:
X(2 + x)(x + -1(2 + i)) = 0
X(2 + x)(x + (2 * -1 + i * -1)) = 0
X(2 + x)(x + (-2 + -1i)) = 0

Reorder the terms:
X(2 + x)(-2 + -1i + x) = 0

Multiply (2 + x) * (-2 + -1i + x)
X(2(-2 + -1i + x) + x(-2 + -1i + x)) = 0
X((-2 * 2 + -1i * 2 + x * 2) + x(-2 + -1i + x)) = 0
X((-4 + -2i + 2x) + x(-2 + -1i + x)) = 0
X(-4 + -2i + 2x + (-2 * x + -1i * x + x * x)) = 0

Reorder the terms:
X(-4 + -2i + 2x + (-1ix + -2x + x2)) = 0
X(-4 + -2i + 2x + (-1ix + -2x + x2)) = 0

Reorder the terms:
X(-4 + -2i + -1ix + 2x + -2x + x2) = 0

Combine like terms: 2x + -2x = 0
X(-4 + -2i + -1ix + 0 + x2) = 0
X(-4 + -2i + -1ix + x2) = 0
(-4 * X + -2i * X + -1ix * X + x2 * X) = 0
(-4X + -2iX + -1ixX + x2X) = 0

Solving
-4X + -2iX + -1ixX + x2X = 0

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'X'.
X(-4 + -2i + -1ix + x2) = 0

Subproblem 1
Set the factor 'X' equal to zero and attempt to solve:

Simplifying
X = 0

Solving
X = 0

Move all terms containing X to the left, all other terms to the right.

Simplifying
X = 0
Subproblem 2
Set the factor '(-4 + -2i + -1ix + x2)' equal to zero and attempt to solve:

Simplifying
-4 + -2i + -1ix + x2 = 0

Solving
-4 + -2i + -1ix + x2 = 0

Move all terms containing X to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + -2i + -1ix + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2i + -1ix + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2i + -1ix + x2 = 0 + 4
-2i + -1ix + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2i + -1ix + x2 = 4

Add '2i' to each side of the equation.
-2i + -1ix + 2i + x2 = 4 + 2i

Reorder the terms:
-2i + 2i + -1ix + x2 = 4 + 2i

Combine like terms: -2i + 2i = 0
0 + -1ix + x2 = 4 + 2i
-1ix + x2 = 4 + 2i

Add 'ix' to each side of the equation.
-1ix + ix + x2 = 4 + 2i + ix

Combine like terms: -1ix + ix = 0
0 + x2 = 4 + 2i + ix
x2 = 4 + 2i + ix

Add '-1x2' to each side of the equation.
x2 + -1x2 = 4 + 2i + ix + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 4 + 2i + ix + -1x2

Simplifying
0 = 4 + 2i + ix + -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}