(x-2)(x-10i)(x+10i)=0

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Solution for (x-2)(x-10i)(x+10i)=0 equation: 


Simplifying
(x + -2)(x + -10i)(x + 10i) = 0

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

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

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

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

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

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

Reorder the terms:
((20ix + 200i2) + -10ix * (10i + x) + -2x * (10i + x) + x2(10i + x)) = 0
((20ix + 200i2) + -10ix * (10i + x) + -2x * (10i + x) + x2(10i + x)) = 0
(20ix + 200i2 + (10i * -10ix + x * -10ix) + -2x * (10i + x) + x2(10i + x)) = 0

Reorder the terms:
(20ix + 200i2 + (-10ix2 + -100i2x) + -2x * (10i + x) + x2(10i + x)) = 0
(20ix + 200i2 + (-10ix2 + -100i2x) + -2x * (10i + x) + x2(10i + x)) = 0
(20ix + 200i2 + -10ix2 + -100i2x + (10i * -2x + x * -2x) + x2(10i + x)) = 0
(20ix + 200i2 + -10ix2 + -100i2x + (-20ix + -2x2) + x2(10i + x)) = 0
(20ix + 200i2 + -10ix2 + -100i2x + -20ix + -2x2 + (10i * x2 + x * x2)) = 0
(20ix + 200i2 + -10ix2 + -100i2x + -20ix + -2x2 + (10ix2 + x3)) = 0

Reorder the terms:
(20ix + -20ix + -10ix2 + 10ix2 + 200i2 + -100i2x + -2x2 + x3) = 0

Combine like terms: 20ix + -20ix = 0
(0 + -10ix2 + 10ix2 + 200i2 + -100i2x + -2x2 + x3) = 0
(-10ix2 + 10ix2 + 200i2 + -100i2x + -2x2 + x3) = 0

Combine like terms: -10ix2 + 10ix2 = 0
(0 + 200i2 + -100i2x + -2x2 + x3) = 0
(200i2 + -100i2x + -2x2 + x3) = 0

Solving
200i2 + -100i2x + -2x2 + x3 = 0

Solving for variable 'i'.

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

Add '2x2' to each side of the equation.
200i2 + -100i2x + -2x2 + 2x2 + x3 = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
200i2 + -100i2x + 0 + x3 = 0 + 2x2
200i2 + -100i2x + x3 = 0 + 2x2
Remove the zero:
200i2 + -100i2x + x3 = 2x2

Add '-1x3' to each side of the equation.
200i2 + -100i2x + x3 + -1x3 = 2x2 + -1x3

Combine like terms: x3 + -1x3 = 0
200i2 + -100i2x + 0 = 2x2 + -1x3
200i2 + -100i2x = 2x2 + -1x3

Reorder the terms:
200i2 + -100i2x + -2x2 + x3 = 2x2 + -2x2 + -1x3 + x3

Combine like terms: 2x2 + -2x2 = 0
200i2 + -100i2x + -2x2 + x3 = 0 + -1x3 + x3
200i2 + -100i2x + -2x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
200i2 + -100i2x + -2x2 + x3 = 0

The solution to this equation could not be determined.

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