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

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


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

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

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

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

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

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

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

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

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

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

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

Combine like terms: 2ix2 + -2ix2 = 0
(0 + 20i2 + -4i2x + -5x2 + x3) = 0
(20i2 + -4i2x + -5x2 + x3) = 0

Solving
20i2 + -4i2x + -5x2 + x3 = 0

Solving for variable 'i'.

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

Add '5x2' to each side of the equation.
20i2 + -4i2x + -5x2 + 5x2 + x3 = 0 + 5x2

Combine like terms: -5x2 + 5x2 = 0
20i2 + -4i2x + 0 + x3 = 0 + 5x2
20i2 + -4i2x + x3 = 0 + 5x2
Remove the zero:
20i2 + -4i2x + x3 = 5x2

Add '-1x3' to each side of the equation.
20i2 + -4i2x + x3 + -1x3 = 5x2 + -1x3

Combine like terms: x3 + -1x3 = 0
20i2 + -4i2x + 0 = 5x2 + -1x3
20i2 + -4i2x = 5x2 + -1x3

Reorder the terms:
20i2 + -4i2x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3

Combine like terms: 5x2 + -5x2 = 0
20i2 + -4i2x + -5x2 + x3 = 0 + -1x3 + x3
20i2 + -4i2x + -5x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
20i2 + -4i2x + -5x2 + x3 = 0

The solution to this equation could not be determined.

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