Y=(x-5)(x-(3+2i))(x-(3-2i))

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Solution for Y=(x-5)(x-(3+2i))(x-(3-2i)) equation: 


Simplifying
Y = (x + -5)(x + -1(3 + 2i))(x + -1(3 + -2i))

Reorder the terms:
Y = (-5 + x)(x + -1(3 + 2i))(x + -1(3 + -2i))
Y = (-5 + x)(x + (3 * -1 + 2i * -1))(x + -1(3 + -2i))
Y = (-5 + x)(x + (-3 + -2i))(x + -1(3 + -2i))

Reorder the terms:
Y = (-5 + x)(-3 + -2i + x)(x + -1(3 + -2i))
Y = (-5 + x)(-3 + -2i + x)(x + (3 * -1 + -2i * -1))
Y = (-5 + x)(-3 + -2i + x)(x + (-3 + 2i))

Reorder the terms:
Y = (-5 + x)(-3 + -2i + x)(-3 + 2i + x)

Multiply (-5 + x) * (-3 + -2i + x)
Y = (-5(-3 + -2i + x) + x(-3 + -2i + x))(-3 + 2i + x)
Y = ((-3 * -5 + -2i * -5 + x * -5) + x(-3 + -2i + x))(-3 + 2i + x)
Y = ((15 + 10i + -5x) + x(-3 + -2i + x))(-3 + 2i + x)
Y = (15 + 10i + -5x + (-3 * x + -2i * x + x * x))(-3 + 2i + x)

Reorder the terms:
Y = (15 + 10i + -5x + (-2ix + -3x + x2))(-3 + 2i + x)
Y = (15 + 10i + -5x + (-2ix + -3x + x2))(-3 + 2i + x)

Reorder the terms:
Y = (15 + 10i + -2ix + -5x + -3x + x2)(-3 + 2i + x)

Combine like terms: -5x + -3x = -8x
Y = (15 + 10i + -2ix + -8x + x2)(-3 + 2i + x)

Multiply (15 + 10i + -2ix + -8x + x2) * (-3 + 2i + x)
Y = (15(-3 + 2i + x) + 10i * (-3 + 2i + x) + -2ix * (-3 + 2i + x) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = ((-3 * 15 + 2i * 15 + x * 15) + 10i * (-3 + 2i + x) + -2ix * (-3 + 2i + x) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = ((-45 + 30i + 15x) + 10i * (-3 + 2i + x) + -2ix * (-3 + 2i + x) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-45 + 30i + 15x + (-3 * 10i + 2i * 10i + x * 10i) + -2ix * (-3 + 2i + x) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))

Reorder the terms:
Y = (-45 + 30i + 15x + (-30i + 10ix + 20i2) + -2ix * (-3 + 2i + x) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-45 + 30i + 15x + (-30i + 10ix + 20i2) + -2ix * (-3 + 2i + x) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + (-3 * -2ix + 2i * -2ix + x * -2ix) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))

Reorder the terms:
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + (6ix + -2ix2 + -4i2x) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + (6ix + -2ix2 + -4i2x) + -8x * (-3 + 2i + x) + x2(-3 + 2i + x))
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + 6ix + -2ix2 + -4i2x + (-3 * -8x + 2i * -8x + x * -8x) + x2(-3 + 2i + x))

Reorder the terms:
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + 6ix + -2ix2 + -4i2x + (-16ix + 24x + -8x2) + x2(-3 + 2i + x))
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + 6ix + -2ix2 + -4i2x + (-16ix + 24x + -8x2) + x2(-3 + 2i + x))
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + 6ix + -2ix2 + -4i2x + -16ix + 24x + -8x2 + (-3 * x2 + 2i * x2 + x * x2))

Reorder the terms:
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + 6ix + -2ix2 + -4i2x + -16ix + 24x + -8x2 + (2ix2 + -3x2 + x3))
Y = (-45 + 30i + 15x + -30i + 10ix + 20i2 + 6ix + -2ix2 + -4i2x + -16ix + 24x + -8x2 + (2ix2 + -3x2 + x3))

Reorder the terms:
Y = (-45 + 30i + -30i + 10ix + 6ix + -16ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 15x + 24x + -8x2 + -3x2 + x3)

Combine like terms: 30i + -30i = 0
Y = (-45 + 0 + 10ix + 6ix + -16ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 15x + 24x + -8x2 + -3x2 + x3)
Y = (-45 + 10ix + 6ix + -16ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 15x + 24x + -8x2 + -3x2 + x3)

Combine like terms: 10ix + 6ix = 16ix
Y = (-45 + 16ix + -16ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 15x + 24x + -8x2 + -3x2 + x3)

Combine like terms: 16ix + -16ix = 0
Y = (-45 + 0 + -2ix2 + 2ix2 + 20i2 + -4i2x + 15x + 24x + -8x2 + -3x2 + x3)
Y = (-45 + -2ix2 + 2ix2 + 20i2 + -4i2x + 15x + 24x + -8x2 + -3x2 + x3)

Combine like terms: -2ix2 + 2ix2 = 0
Y = (-45 + 0 + 20i2 + -4i2x + 15x + 24x + -8x2 + -3x2 + x3)
Y = (-45 + 20i2 + -4i2x + 15x + 24x + -8x2 + -3x2 + x3)

Combine like terms: 15x + 24x = 39x
Y = (-45 + 20i2 + -4i2x + 39x + -8x2 + -3x2 + x3)

Combine like terms: -8x2 + -3x2 = -11x2
Y = (-45 + 20i2 + -4i2x + 39x + -11x2 + x3)

Solving
Y = -45 + 20i2 + -4i2x + 39x + -11x2 + x3

Solving for variable 'Y'.

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

Simplifying
Y = -45 + 20i2 + -4i2x + 39x + -11x2 + x3

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