(x-5-5i)(x-5i+5i)(x+4)=0

Solution for (x-5-5i)(x-5i+5i)(x+4)=0 equation:

Simplifying
(x + -5 + -5i)(x + -5i + 5i)(x + 4) = 0

Reorder the terms:
(-5 + -5i + x)(x + -5i + 5i)(x + 4) = 0

Reorder the terms:
(-5 + -5i + x)(-5i + 5i + x)(x + 4) = 0

Combine like terms: -5i + 5i = 0
(-5 + -5i + x)(0 + x)(x + 4) = 0
(-5 + -5i + x)(x)(x + 4) = 0

Reorder the terms:
(-5 + -5i + x) * x(4 + x) = 0

Reorder the terms for easier multiplication:
x(-5 + -5i + x)(4 + x) = 0

Multiply (-5 + -5i + x) * (4 + x)
x(-5(4 + x) + -5i * (4 + x) + x(4 + x)) = 0
x((4 * -5 + x * -5) + -5i * (4 + x) + x(4 + x)) = 0
x((-20 + -5x) + -5i * (4 + x) + x(4 + x)) = 0
x(-20 + -5x + (4 * -5i + x * -5i) + x(4 + x)) = 0
x(-20 + -5x + (-20i + -5ix) + x(4 + x)) = 0
x(-20 + -5x + -20i + -5ix + (4 * x + x * x)) = 0
x(-20 + -5x + -20i + -5ix + (4x + x2)) = 0

Reorder the terms:
x(-20 + -20i + -5ix + -5x + 4x + x2) = 0

Combine like terms: -5x + 4x = -1x
x(-20 + -20i + -5ix + -1x + x2) = 0
(-20 * x + -20i * x + -5ix * x + -1x * x + x2 * x) = 0

Reorder the terms:
(-20ix + -5ix2 + -20x + -1x2 + x3) = 0
(-20ix + -5ix2 + -20x + -1x2 + x3) = 0

Solving
-20ix + -5ix2 + -20x + -1x2 + x3 = 0

Solving for variable 'i'.

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

Add '20x' to each side of the equation.
-20ix + -5ix2 + -20x + -1x2 + 20x + x3 = 0 + 20x

Reorder the terms:
-20ix + -5ix2 + -20x + 20x + -1x2 + x3 = 0 + 20x

Combine like terms: -20x + 20x = 0
-20ix + -5ix2 + 0 + -1x2 + x3 = 0 + 20x
-20ix + -5ix2 + -1x2 + x3 = 0 + 20x
Remove the zero:
-20ix + -5ix2 + -1x2 + x3 = 20x

Add 'x2' to each side of the equation.
-20ix + -5ix2 + -1x2 + x2 + x3 = 20x + x2

Combine like terms: -1x2 + x2 = 0
-20ix + -5ix2 + 0 + x3 = 20x + x2
-20ix + -5ix2 + x3 = 20x + x2

Add '-1x3' to each side of the equation.
-20ix + -5ix2 + x3 + -1x3 = 20x + x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-20ix + -5ix2 + 0 = 20x + x2 + -1x3
-20ix + -5ix2 = 20x + x2 + -1x3

Reorder the terms:
-20ix + -5ix2 + -20x + -1x2 + x3 = 20x + -20x + x2 + -1x2 + -1x3 + x3

Combine like terms: 20x + -20x = 0
-20ix + -5ix2 + -20x + -1x2 + x3 = 0 + x2 + -1x2 + -1x3 + x3
-20ix + -5ix2 + -20x + -1x2 + x3 = x2 + -1x2 + -1x3 + x3

Combine like terms: x2 + -1x2 = 0
-20ix + -5ix2 + -20x + -1x2 + x3 = 0 + -1x3 + x3
-20ix + -5ix2 + -20x + -1x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-20ix + -5ix2 + -20x + -1x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-20i + -5ix + -20 + -1x + 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 i to the left, all other terms to the right.

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-20i + -5ix + -20 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-20i + -5ix + -20 + -1x + x2 = 0

Reorder the terms:
-20 + -20i + -5ix + -1x + x2 = 0

Solving
-20 + -20i + -5ix + -1x + x2 = 0

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

Add '20' to each side of the equation.
-20 + -20i + -5ix + -1x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -20i + -5ix + -1x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -20i + -5ix + -1x + x2 = 0 + 20
-20i + -5ix + -1x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-20i + -5ix + -1x + x2 = 20

Add 'x' to each side of the equation.
-20i + -5ix + -1x + x + x2 = 20 + x

Combine like terms: -1x + x = 0
-20i + -5ix + 0 + x2 = 20 + x
-20i + -5ix + x2 = 20 + x

Add '-1x2' to each side of the equation.
-20i + -5ix + x2 + -1x2 = 20 + x + -1x2

Combine like terms: x2 + -1x2 = 0
-20i + -5ix + 0 = 20 + x + -1x2
-20i + -5ix = 20 + x + -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.