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Simplifying y = (x + -1(4 + i))(x + -1(4 + -1i))(x + -2) y = (x + (4 * -1 + i * -1))(x + -1(4 + -1i))(x + -2) y = (x + (-4 + -1i))(x + -1(4 + -1i))(x + -2) Reorder the terms: y = (-4 + -1i + x)(x + -1(4 + -1i))(x + -2) y = (-4 + -1i + x)(x + (4 * -1 + -1i * -1))(x + -2) y = (-4 + -1i + x)(x + (-4 + 1i))(x + -2) Reorder the terms: y = (-4 + -1i + x)(-4 + 1i + x)(x + -2) Reorder the terms: y = (-4 + -1i + x)(-4 + 1i + x)(-2 + x) Multiply (-4 + -1i + x) * (-4 + 1i + x) y = (-4(-4 + 1i + x) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-2 + x) y = ((-4 * -4 + 1i * -4 + x * -4) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-2 + x) y = ((16 + -4i + -4x) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-2 + x) y = (16 + -4i + -4x + (-4 * -1i + 1i * -1i + x * -1i) + x(-4 + 1i + x))(-2 + x) Reorder the terms: y = (16 + -4i + -4x + (4i + -1ix + -1i2) + x(-4 + 1i + x))(-2 + x) y = (16 + -4i + -4x + (4i + -1ix + -1i2) + x(-4 + 1i + x))(-2 + x) y = (16 + -4i + -4x + 4i + -1ix + -1i2 + (-4 * x + 1i * x + x * x))(-2 + x) Reorder the terms: y = (16 + -4i + -4x + 4i + -1ix + -1i2 + (1ix + -4x + x2))(-2 + x) y = (16 + -4i + -4x + 4i + -1ix + -1i2 + (1ix + -4x + x2))(-2 + x) Reorder the terms: y = (16 + -4i + 4i + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-2 + x) Combine like terms: -4i + 4i = 0 y = (16 + 0 + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-2 + x) y = (16 + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-2 + x) Combine like terms: -1ix + 1ix = 0 y = (16 + 0 + -1i2 + -4x + -4x + x2)(-2 + x) y = (16 + -1i2 + -4x + -4x + x2)(-2 + x) Combine like terms: -4x + -4x = -8x y = (16 + -1i2 + -8x + x2)(-2 + x) Multiply (16 + -1i2 + -8x + x2) * (-2 + x) y = (16(-2 + x) + -1i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x)) y = ((-2 * 16 + x * 16) + -1i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x)) y = ((-32 + 16x) + -1i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x)) y = (-32 + 16x + (-2 * -1i2 + x * -1i2) + -8x * (-2 + x) + x2(-2 + x)) y = (-32 + 16x + (2i2 + -1i2x) + -8x * (-2 + x) + x2(-2 + x)) y = (-32 + 16x + 2i2 + -1i2x + (-2 * -8x + x * -8x) + x2(-2 + x)) y = (-32 + 16x + 2i2 + -1i2x + (16x + -8x2) + x2(-2 + x)) y = (-32 + 16x + 2i2 + -1i2x + 16x + -8x2 + (-2 * x2 + x * x2)) y = (-32 + 16x + 2i2 + -1i2x + 16x + -8x2 + (-2x2 + x3)) Reorder the terms: y = (-32 + 2i2 + -1i2x + 16x + 16x + -8x2 + -2x2 + x3) Combine like terms: 16x + 16x = 32x y = (-32 + 2i2 + -1i2x + 32x + -8x2 + -2x2 + x3) Combine like terms: -8x2 + -2x2 = -10x2 y = (-32 + 2i2 + -1i2x + 32x + -10x2 + x3) Solving y = -32 + 2i2 + -1i2x + 32x + -10x2 + x3 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Simplifying y = -32 + 2i2 + -1i2x + 32x + -10x2 + x3
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