(x+2)(x-2+5i)(x-2-5i)=0

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Solution for (x+2)(x-2+5i)(x-2-5i)=0 equation: 


Simplifying
(x + 2)(x + -2 + 5i)(x + -2 + -5i) = 0

Reorder the terms:
(2 + x)(x + -2 + 5i)(x + -2 + -5i) = 0

Reorder the terms:
(2 + x)(-2 + 5i + x)(x + -2 + -5i) = 0

Reorder the terms:
(2 + x)(-2 + 5i + x)(-2 + -5i + x) = 0

Multiply (2 + x) * (-2 + 5i + x)
(2(-2 + 5i + x) + x(-2 + 5i + x))(-2 + -5i + x) = 0
((-2 * 2 + 5i * 2 + x * 2) + x(-2 + 5i + x))(-2 + -5i + x) = 0
((-4 + 10i + 2x) + x(-2 + 5i + x))(-2 + -5i + x) = 0
(-4 + 10i + 2x + (-2 * x + 5i * x + x * x))(-2 + -5i + x) = 0

Reorder the terms:
(-4 + 10i + 2x + (5ix + -2x + x2))(-2 + -5i + x) = 0
(-4 + 10i + 2x + (5ix + -2x + x2))(-2 + -5i + x) = 0

Reorder the terms:
(-4 + 10i + 5ix + 2x + -2x + x2)(-2 + -5i + x) = 0

Combine like terms: 2x + -2x = 0
(-4 + 10i + 5ix + 0 + x2)(-2 + -5i + x) = 0
(-4 + 10i + 5ix + x2)(-2 + -5i + x) = 0

Multiply (-4 + 10i + 5ix + x2) * (-2 + -5i + x)
(-4(-2 + -5i + x) + 10i * (-2 + -5i + x) + 5ix * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
((-2 * -4 + -5i * -4 + x * -4) + 10i * (-2 + -5i + x) + 5ix * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
((8 + 20i + -4x) + 10i * (-2 + -5i + x) + 5ix * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
(8 + 20i + -4x + (-2 * 10i + -5i * 10i + x * 10i) + 5ix * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0

Reorder the terms:
(8 + 20i + -4x + (-20i + 10ix + -50i2) + 5ix * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
(8 + 20i + -4x + (-20i + 10ix + -50i2) + 5ix * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
(8 + 20i + -4x + -20i + 10ix + -50i2 + (-2 * 5ix + -5i * 5ix + x * 5ix) + x2(-2 + -5i + x)) = 0

Reorder the terms:
(8 + 20i + -4x + -20i + 10ix + -50i2 + (-10ix + 5ix2 + -25i2x) + x2(-2 + -5i + x)) = 0
(8 + 20i + -4x + -20i + 10ix + -50i2 + (-10ix + 5ix2 + -25i2x) + x2(-2 + -5i + x)) = 0
(8 + 20i + -4x + -20i + 10ix + -50i2 + -10ix + 5ix2 + -25i2x + (-2 * x2 + -5i * x2 + x * x2)) = 0

Reorder the terms:
(8 + 20i + -4x + -20i + 10ix + -50i2 + -10ix + 5ix2 + -25i2x + (-5ix2 + -2x2 + x3)) = 0
(8 + 20i + -4x + -20i + 10ix + -50i2 + -10ix + 5ix2 + -25i2x + (-5ix2 + -2x2 + x3)) = 0

Reorder the terms:
(8 + 20i + -20i + 10ix + -10ix + 5ix2 + -5ix2 + -50i2 + -25i2x + -4x + -2x2 + x3) = 0

Combine like terms: 20i + -20i = 0
(8 + 0 + 10ix + -10ix + 5ix2 + -5ix2 + -50i2 + -25i2x + -4x + -2x2 + x3) = 0
(8 + 10ix + -10ix + 5ix2 + -5ix2 + -50i2 + -25i2x + -4x + -2x2 + x3) = 0

Combine like terms: 10ix + -10ix = 0
(8 + 0 + 5ix2 + -5ix2 + -50i2 + -25i2x + -4x + -2x2 + x3) = 0
(8 + 5ix2 + -5ix2 + -50i2 + -25i2x + -4x + -2x2 + x3) = 0

Combine like terms: 5ix2 + -5ix2 = 0
(8 + 0 + -50i2 + -25i2x + -4x + -2x2 + x3) = 0
(8 + -50i2 + -25i2x + -4x + -2x2 + x3) = 0

Solving
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = 0

Solving for variable 'i'.

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

Add '-8' to each side of the equation.
8 + -50i2 + -25i2x + -4x + -2x2 + -8 + x3 = 0 + -8

Reorder the terms:
8 + -8 + -50i2 + -25i2x + -4x + -2x2 + x3 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -50i2 + -25i2x + -4x + -2x2 + x3 = 0 + -8
-50i2 + -25i2x + -4x + -2x2 + x3 = 0 + -8

Combine like terms: 0 + -8 = -8
-50i2 + -25i2x + -4x + -2x2 + x3 = -8

Add '4x' to each side of the equation.
-50i2 + -25i2x + -4x + -2x2 + 4x + x3 = -8 + 4x

Reorder the terms:
-50i2 + -25i2x + -4x + 4x + -2x2 + x3 = -8 + 4x

Combine like terms: -4x + 4x = 0
-50i2 + -25i2x + 0 + -2x2 + x3 = -8 + 4x
-50i2 + -25i2x + -2x2 + x3 = -8 + 4x

Add '2x2' to each side of the equation.
-50i2 + -25i2x + -2x2 + 2x2 + x3 = -8 + 4x + 2x2

Combine like terms: -2x2 + 2x2 = 0
-50i2 + -25i2x + 0 + x3 = -8 + 4x + 2x2
-50i2 + -25i2x + x3 = -8 + 4x + 2x2

Add '-1x3' to each side of the equation.
-50i2 + -25i2x + x3 + -1x3 = -8 + 4x + 2x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-50i2 + -25i2x + 0 = -8 + 4x + 2x2 + -1x3
-50i2 + -25i2x = -8 + 4x + 2x2 + -1x3

Reorder the terms:
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = -8 + 4x + 2x2 + -1x3 + 8 + -4x + -2x2 + x3

Reorder the terms:
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = -8 + 8 + 4x + -4x + 2x2 + -2x2 + -1x3 + x3

Combine like terms: -8 + 8 = 0
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = 0 + 4x + -4x + 2x2 + -2x2 + -1x3 + x3
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = 4x + -4x + 2x2 + -2x2 + -1x3 + x3

Combine like terms: 4x + -4x = 0
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = 0 + 2x2 + -2x2 + -1x3 + x3
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = 2x2 + -2x2 + -1x3 + x3

Combine like terms: 2x2 + -2x2 = 0
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = 0 + -1x3 + x3
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
8 + -50i2 + -25i2x + -4x + -2x2 + x3 = 0

The solution to this equation could not be determined.

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