(x-3)(x-10i)(x+10i)=0

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Solution for (x-3)(x-10i)(x+10i)=0 equation: 


Simplifying
(x + -3)(x + -10i)(x + 10i) = 0

Reorder the terms:
(-3 + x)(x + -10i)(x + 10i) = 0

Reorder the terms:
(-3 + x)(-10i + x)(x + 10i) = 0

Reorder the terms:
(-3 + x)(-10i + x)(10i + x) = 0

Multiply (-3 + x) * (-10i + x)
(-3(-10i + x) + x(-10i + x))(10i + x) = 0
((-10i * -3 + x * -3) + x(-10i + x))(10i + x) = 0
((30i + -3x) + x(-10i + x))(10i + x) = 0
(30i + -3x + (-10i * x + x * x))(10i + x) = 0
(30i + -3x + (-10ix + x2))(10i + x) = 0

Reorder the terms:
(30i + -10ix + -3x + x2)(10i + x) = 0
(30i + -10ix + -3x + x2)(10i + x) = 0

Multiply (30i + -10ix + -3x + x2) * (10i + x)
(30i * (10i + x) + -10ix * (10i + x) + -3x * (10i + x) + x2(10i + x)) = 0
((10i * 30i + x * 30i) + -10ix * (10i + x) + -3x * (10i + x) + x2(10i + x)) = 0

Reorder the terms:
((30ix + 300i2) + -10ix * (10i + x) + -3x * (10i + x) + x2(10i + x)) = 0
((30ix + 300i2) + -10ix * (10i + x) + -3x * (10i + x) + x2(10i + x)) = 0
(30ix + 300i2 + (10i * -10ix + x * -10ix) + -3x * (10i + x) + x2(10i + x)) = 0

Reorder the terms:
(30ix + 300i2 + (-10ix2 + -100i2x) + -3x * (10i + x) + x2(10i + x)) = 0
(30ix + 300i2 + (-10ix2 + -100i2x) + -3x * (10i + x) + x2(10i + x)) = 0
(30ix + 300i2 + -10ix2 + -100i2x + (10i * -3x + x * -3x) + x2(10i + x)) = 0
(30ix + 300i2 + -10ix2 + -100i2x + (-30ix + -3x2) + x2(10i + x)) = 0
(30ix + 300i2 + -10ix2 + -100i2x + -30ix + -3x2 + (10i * x2 + x * x2)) = 0
(30ix + 300i2 + -10ix2 + -100i2x + -30ix + -3x2 + (10ix2 + x3)) = 0

Reorder the terms:
(30ix + -30ix + -10ix2 + 10ix2 + 300i2 + -100i2x + -3x2 + x3) = 0

Combine like terms: 30ix + -30ix = 0
(0 + -10ix2 + 10ix2 + 300i2 + -100i2x + -3x2 + x3) = 0
(-10ix2 + 10ix2 + 300i2 + -100i2x + -3x2 + x3) = 0

Combine like terms: -10ix2 + 10ix2 = 0
(0 + 300i2 + -100i2x + -3x2 + x3) = 0
(300i2 + -100i2x + -3x2 + x3) = 0

Solving
300i2 + -100i2x + -3x2 + x3 = 0

Solving for variable 'i'.

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

Add '3x2' to each side of the equation.
300i2 + -100i2x + -3x2 + 3x2 + x3 = 0 + 3x2

Combine like terms: -3x2 + 3x2 = 0
300i2 + -100i2x + 0 + x3 = 0 + 3x2
300i2 + -100i2x + x3 = 0 + 3x2
Remove the zero:
300i2 + -100i2x + x3 = 3x2

Add '-1x3' to each side of the equation.
300i2 + -100i2x + x3 + -1x3 = 3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
300i2 + -100i2x + 0 = 3x2 + -1x3
300i2 + -100i2x = 3x2 + -1x3

Reorder the terms:
300i2 + -100i2x + -3x2 + x3 = 3x2 + -3x2 + -1x3 + x3

Combine like terms: 3x2 + -3x2 = 0
300i2 + -100i2x + -3x2 + x3 = 0 + -1x3 + x3
300i2 + -100i2x + -3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
300i2 + -100i2x + -3x2 + x3 = 0

The solution to this equation could not be determined.

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