Y=(x-4-3i)(x-4+3i)(x-2)(x-1)

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Solution for Y=(x-4-3i)(x-4+3i)(x-2)(x-1) equation:


Simplifying
Y = (x + -4 + -3i)(x + -4 + 3i)(x + -2)(x + -1)

Reorder the terms:
Y = (-4 + -3i + x)(x + -4 + 3i)(x + -2)(x + -1)

Reorder the terms:
Y = (-4 + -3i + x)(-4 + 3i + x)(x + -2)(x + -1)

Reorder the terms:
Y = (-4 + -3i + x)(-4 + 3i + x)(-2 + x)(x + -1)

Reorder the terms:
Y = (-4 + -3i + x)(-4 + 3i + x)(-2 + x)(-1 + x)

Multiply (-4 + -3i + x) * (-4 + 3i + x)
Y = (-4(-4 + 3i + x) + -3i * (-4 + 3i + x) + x(-4 + 3i + x))(-2 + x)(-1 + x)
Y = ((-4 * -4 + 3i * -4 + x * -4) + -3i * (-4 + 3i + x) + x(-4 + 3i + x))(-2 + x)(-1 + x)
Y = ((16 + -12i + -4x) + -3i * (-4 + 3i + x) + x(-4 + 3i + x))(-2 + x)(-1 + x)
Y = (16 + -12i + -4x + (-4 * -3i + 3i * -3i + x * -3i) + x(-4 + 3i + x))(-2 + x)(-1 + x)

Reorder the terms:
Y = (16 + -12i + -4x + (12i + -3ix + -9i2) + x(-4 + 3i + x))(-2 + x)(-1 + x)
Y = (16 + -12i + -4x + (12i + -3ix + -9i2) + x(-4 + 3i + x))(-2 + x)(-1 + x)
Y = (16 + -12i + -4x + 12i + -3ix + -9i2 + (-4 * x + 3i * x + x * x))(-2 + x)(-1 + x)

Reorder the terms:
Y = (16 + -12i + -4x + 12i + -3ix + -9i2 + (3ix + -4x + x2))(-2 + x)(-1 + x)
Y = (16 + -12i + -4x + 12i + -3ix + -9i2 + (3ix + -4x + x2))(-2 + x)(-1 + x)

Reorder the terms:
Y = (16 + -12i + 12i + -3ix + 3ix + -9i2 + -4x + -4x + x2)(-2 + x)(-1 + x)

Combine like terms: -12i + 12i = 0
Y = (16 + 0 + -3ix + 3ix + -9i2 + -4x + -4x + x2)(-2 + x)(-1 + x)
Y = (16 + -3ix + 3ix + -9i2 + -4x + -4x + x2)(-2 + x)(-1 + x)

Combine like terms: -3ix + 3ix = 0
Y = (16 + 0 + -9i2 + -4x + -4x + x2)(-2 + x)(-1 + x)
Y = (16 + -9i2 + -4x + -4x + x2)(-2 + x)(-1 + x)

Combine like terms: -4x + -4x = -8x
Y = (16 + -9i2 + -8x + x2)(-2 + x)(-1 + x)

Multiply (16 + -9i2 + -8x + x2) * (-2 + x)
Y = (16(-2 + x) + -9i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x))(-1 + x)
Y = ((-2 * 16 + x * 16) + -9i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x))(-1 + x)
Y = ((-32 + 16x) + -9i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x))(-1 + x)
Y = (-32 + 16x + (-2 * -9i2 + x * -9i2) + -8x * (-2 + x) + x2(-2 + x))(-1 + x)
Y = (-32 + 16x + (18i2 + -9i2x) + -8x * (-2 + x) + x2(-2 + x))(-1 + x)
Y = (-32 + 16x + 18i2 + -9i2x + (-2 * -8x + x * -8x) + x2(-2 + x))(-1 + x)
Y = (-32 + 16x + 18i2 + -9i2x + (16x + -8x2) + x2(-2 + x))(-1 + x)
Y = (-32 + 16x + 18i2 + -9i2x + 16x + -8x2 + (-2 * x2 + x * x2))(-1 + x)
Y = (-32 + 16x + 18i2 + -9i2x + 16x + -8x2 + (-2x2 + x3))(-1 + x)

Reorder the terms:
Y = (-32 + 18i2 + -9i2x + 16x + 16x + -8x2 + -2x2 + x3)(-1 + x)

Combine like terms: 16x + 16x = 32x
Y = (-32 + 18i2 + -9i2x + 32x + -8x2 + -2x2 + x3)(-1 + x)

Combine like terms: -8x2 + -2x2 = -10x2
Y = (-32 + 18i2 + -9i2x + 32x + -10x2 + x3)(-1 + x)

Multiply (-32 + 18i2 + -9i2x + 32x + -10x2 + x3) * (-1 + x)
Y = (-32(-1 + x) + 18i2 * (-1 + x) + -9i2x * (-1 + x) + 32x * (-1 + x) + -10x2 * (-1 + x) + x3(-1 + x))
Y = ((-1 * -32 + x * -32) + 18i2 * (-1 + x) + -9i2x * (-1 + x) + 32x * (-1 + x) + -10x2 * (-1 + x) + x3(-1 + x))
Y = ((32 + -32x) + 18i2 * (-1 + x) + -9i2x * (-1 + x) + 32x * (-1 + x) + -10x2 * (-1 + x) + x3(-1 + x))
Y = (32 + -32x + (-1 * 18i2 + x * 18i2) + -9i2x * (-1 + x) + 32x * (-1 + x) + -10x2 * (-1 + x) + x3(-1 + x))
Y = (32 + -32x + (-18i2 + 18i2x) + -9i2x * (-1 + x) + 32x * (-1 + x) + -10x2 * (-1 + x) + x3(-1 + x))
Y = (32 + -32x + -18i2 + 18i2x + (-1 * -9i2x + x * -9i2x) + 32x * (-1 + x) + -10x2 * (-1 + x) + x3(-1 + x))
Y = (32 + -32x + -18i2 + 18i2x + (9i2x + -9i2x2) + 32x * (-1 + x) + -10x2 * (-1 + x) + x3(-1 + x))
Y = (32 + -32x + -18i2 + 18i2x + 9i2x + -9i2x2 + (-1 * 32x + x * 32x) + -10x2 * (-1 + x) + x3(-1 + x))
Y = (32 + -32x + -18i2 + 18i2x + 9i2x + -9i2x2 + (-32x + 32x2) + -10x2 * (-1 + x) + x3(-1 + x))
Y = (32 + -32x + -18i2 + 18i2x + 9i2x + -9i2x2 + -32x + 32x2 + (-1 * -10x2 + x * -10x2) + x3(-1 + x))
Y = (32 + -32x + -18i2 + 18i2x + 9i2x + -9i2x2 + -32x + 32x2 + (10x2 + -10x3) + x3(-1 + x))
Y = (32 + -32x + -18i2 + 18i2x + 9i2x + -9i2x2 + -32x + 32x2 + 10x2 + -10x3 + (-1 * x3 + x * x3))
Y = (32 + -32x + -18i2 + 18i2x + 9i2x + -9i2x2 + -32x + 32x2 + 10x2 + -10x3 + (-1x3 + x4))

Reorder the terms:
Y = (32 + -18i2 + 18i2x + 9i2x + -9i2x2 + -32x + -32x + 32x2 + 10x2 + -10x3 + -1x3 + x4)

Combine like terms: 18i2x + 9i2x = 27i2x
Y = (32 + -18i2 + 27i2x + -9i2x2 + -32x + -32x + 32x2 + 10x2 + -10x3 + -1x3 + x4)

Combine like terms: -32x + -32x = -64x
Y = (32 + -18i2 + 27i2x + -9i2x2 + -64x + 32x2 + 10x2 + -10x3 + -1x3 + x4)

Combine like terms: 32x2 + 10x2 = 42x2
Y = (32 + -18i2 + 27i2x + -9i2x2 + -64x + 42x2 + -10x3 + -1x3 + x4)

Combine like terms: -10x3 + -1x3 = -11x3
Y = (32 + -18i2 + 27i2x + -9i2x2 + -64x + 42x2 + -11x3 + x4)

Solving
Y = 32 + -18i2 + 27i2x + -9i2x2 + -64x + 42x2 + -11x3 + x4

Solving for variable 'Y'.

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

Simplifying
Y = 32 + -18i2 + 27i2x + -9i2x2 + -64x + 42x2 + -11x3 + x4

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