Y=(x-6)(x-(3+2i))(x-(3-2i))

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Solution for Y=(x-6)(x-(3+2i))(x-(3-2i)) equation: 


Simplifying
Y = (x + -6)(x + -1(3 + 2i))(x + -1(3 + -2i))

Reorder the terms:
Y = (-6 + x)(x + -1(3 + 2i))(x + -1(3 + -2i))
Y = (-6 + x)(x + (3 * -1 + 2i * -1))(x + -1(3 + -2i))
Y = (-6 + x)(x + (-3 + -2i))(x + -1(3 + -2i))

Reorder the terms:
Y = (-6 + x)(-3 + -2i + x)(x + -1(3 + -2i))
Y = (-6 + x)(-3 + -2i + x)(x + (3 * -1 + -2i * -1))
Y = (-6 + x)(-3 + -2i + x)(x + (-3 + 2i))

Reorder the terms:
Y = (-6 + x)(-3 + -2i + x)(-3 + 2i + x)

Multiply (-6 + x) * (-3 + -2i + x)
Y = (-6(-3 + -2i + x) + x(-3 + -2i + x))(-3 + 2i + x)
Y = ((-3 * -6 + -2i * -6 + x * -6) + x(-3 + -2i + x))(-3 + 2i + x)
Y = ((18 + 12i + -6x) + x(-3 + -2i + x))(-3 + 2i + x)
Y = (18 + 12i + -6x + (-3 * x + -2i * x + x * x))(-3 + 2i + x)

Reorder the terms:
Y = (18 + 12i + -6x + (-2ix + -3x + x2))(-3 + 2i + x)
Y = (18 + 12i + -6x + (-2ix + -3x + x2))(-3 + 2i + x)

Reorder the terms:
Y = (18 + 12i + -2ix + -6x + -3x + x2)(-3 + 2i + x)

Combine like terms: -6x + -3x = -9x
Y = (18 + 12i + -2ix + -9x + x2)(-3 + 2i + x)

Multiply (18 + 12i + -2ix + -9x + x2) * (-3 + 2i + x)
Y = (18(-3 + 2i + x) + 12i * (-3 + 2i + x) + -2ix * (-3 + 2i + x) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = ((-3 * 18 + 2i * 18 + x * 18) + 12i * (-3 + 2i + x) + -2ix * (-3 + 2i + x) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = ((-54 + 36i + 18x) + 12i * (-3 + 2i + x) + -2ix * (-3 + 2i + x) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-54 + 36i + 18x + (-3 * 12i + 2i * 12i + x * 12i) + -2ix * (-3 + 2i + x) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))

Reorder the terms:
Y = (-54 + 36i + 18x + (-36i + 12ix + 24i2) + -2ix * (-3 + 2i + x) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-54 + 36i + 18x + (-36i + 12ix + 24i2) + -2ix * (-3 + 2i + x) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + (-3 * -2ix + 2i * -2ix + x * -2ix) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))

Reorder the terms:
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + (6ix + -2ix2 + -4i2x) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + (6ix + -2ix2 + -4i2x) + -9x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + 6ix + -2ix2 + -4i2x + (-3 * -9x + 2i * -9x + x * -9x) + x2(-3 + 2i + x))

Reorder the terms:
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + 6ix + -2ix2 + -4i2x + (-18ix + 27x + -9x2) + x2(-3 + 2i + x))
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + 6ix + -2ix2 + -4i2x + (-18ix + 27x + -9x2) + x2(-3 + 2i + x))
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + 6ix + -2ix2 + -4i2x + -18ix + 27x + -9x2 + (-3 * x2 + 2i * x2 + x * x2))

Reorder the terms:
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + 6ix + -2ix2 + -4i2x + -18ix + 27x + -9x2 + (2ix2 + -3x2 + x3))
Y = (-54 + 36i + 18x + -36i + 12ix + 24i2 + 6ix + -2ix2 + -4i2x + -18ix + 27x + -9x2 + (2ix2 + -3x2 + x3))

Reorder the terms:
Y = (-54 + 36i + -36i + 12ix + 6ix + -18ix + -2ix2 + 2ix2 + 24i2 + -4i2x + 18x + 27x + -9x2 + -3x2 + x3)

Combine like terms: 36i + -36i = 0
Y = (-54 + 0 + 12ix + 6ix + -18ix + -2ix2 + 2ix2 + 24i2 + -4i2x + 18x + 27x + -9x2 + -3x2 + x3)
Y = (-54 + 12ix + 6ix + -18ix + -2ix2 + 2ix2 + 24i2 + -4i2x + 18x + 27x + -9x2 + -3x2 + x3)

Combine like terms: 12ix + 6ix = 18ix
Y = (-54 + 18ix + -18ix + -2ix2 + 2ix2 + 24i2 + -4i2x + 18x + 27x + -9x2 + -3x2 + x3)

Combine like terms: 18ix + -18ix = 0
Y = (-54 + 0 + -2ix2 + 2ix2 + 24i2 + -4i2x + 18x + 27x + -9x2 + -3x2 + x3)
Y = (-54 + -2ix2 + 2ix2 + 24i2 + -4i2x + 18x + 27x + -9x2 + -3x2 + x3)

Combine like terms: -2ix2 + 2ix2 = 0
Y = (-54 + 0 + 24i2 + -4i2x + 18x + 27x + -9x2 + -3x2 + x3)
Y = (-54 + 24i2 + -4i2x + 18x + 27x + -9x2 + -3x2 + x3)

Combine like terms: 18x + 27x = 45x
Y = (-54 + 24i2 + -4i2x + 45x + -9x2 + -3x2 + x3)

Combine like terms: -9x2 + -3x2 = -12x2
Y = (-54 + 24i2 + -4i2x + 45x + -12x2 + x3)

Solving
Y = -54 + 24i2 + -4i2x + 45x + -12x2 + x3

Solving for variable 'Y'.

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

Simplifying
Y = -54 + 24i2 + -4i2x + 45x + -12x2 + x3

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