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Simplifying (x + 2)(x + -2)(x + -1(1 + -2i))(x + -1(1 + 2i)) = y Reorder the terms: (2 + x)(x + -2)(x + -1(1 + -2i))(x + -1(1 + 2i)) = y Reorder the terms: (2 + x)(-2 + x)(x + -1(1 + -2i))(x + -1(1 + 2i)) = y (2 + x)(-2 + x)(x + (1 * -1 + -2i * -1))(x + -1(1 + 2i)) = y (2 + x)(-2 + x)(x + (-1 + 2i))(x + -1(1 + 2i)) = y Reorder the terms: (2 + x)(-2 + x)(-1 + 2i + x)(x + -1(1 + 2i)) = y (2 + x)(-2 + x)(-1 + 2i + x)(x + (1 * -1 + 2i * -1)) = y (2 + x)(-2 + x)(-1 + 2i + x)(x + (-1 + -2i)) = y Reorder the terms: (2 + x)(-2 + x)(-1 + 2i + x)(-1 + -2i + x) = y Multiply (2 + x) * (-2 + x) (2(-2 + x) + x(-2 + x))(-1 + 2i + x)(-1 + -2i + x) = y ((-2 * 2 + x * 2) + x(-2 + x))(-1 + 2i + x)(-1 + -2i + x) = y ((-4 + 2x) + x(-2 + x))(-1 + 2i + x)(-1 + -2i + x) = y (-4 + 2x + (-2 * x + x * x))(-1 + 2i + x)(-1 + -2i + x) = y (-4 + 2x + (-2x + x2))(-1 + 2i + x)(-1 + -2i + x) = y Combine like terms: 2x + -2x = 0 (-4 + 0 + x2)(-1 + 2i + x)(-1 + -2i + x) = y (-4 + x2)(-1 + 2i + x)(-1 + -2i + x) = y Multiply (-4 + x2) * (-1 + 2i + x) (-4(-1 + 2i + x) + x2(-1 + 2i + x))(-1 + -2i + x) = y ((-1 * -4 + 2i * -4 + x * -4) + x2(-1 + 2i + x))(-1 + -2i + x) = y ((4 + -8i + -4x) + x2(-1 + 2i + x))(-1 + -2i + x) = y (4 + -8i + -4x + (-1 * x2 + 2i * x2 + x * x2))(-1 + -2i + x) = y Reorder the terms: (4 + -8i + -4x + (2ix2 + -1x2 + x3))(-1 + -2i + x) = y (4 + -8i + -4x + (2ix2 + -1x2 + x3))(-1 + -2i + x) = y Reorder the terms: (4 + -8i + 2ix2 + -4x + -1x2 + x3)(-1 + -2i + x) = y (4 + -8i + 2ix2 + -4x + -1x2 + x3)(-1 + -2i + x) = y Multiply (4 + -8i + 2ix2 + -4x + -1x2 + x3) * (-1 + -2i + x) (4(-1 + -2i + x) + -8i * (-1 + -2i + x) + 2ix2 * (-1 + -2i + x) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y ((-1 * 4 + -2i * 4 + x * 4) + -8i * (-1 + -2i + x) + 2ix2 * (-1 + -2i + x) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y ((-4 + -8i + 4x) + -8i * (-1 + -2i + x) + 2ix2 * (-1 + -2i + x) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + (-1 * -8i + -2i * -8i + x * -8i) + 2ix2 * (-1 + -2i + x) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y Reorder the terms: (-4 + -8i + 4x + (8i + -8ix + 16i2) + 2ix2 * (-1 + -2i + x) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + (8i + -8ix + 16i2) + 2ix2 * (-1 + -2i + x) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + 8i + -8ix + 16i2 + (-1 * 2ix2 + -2i * 2ix2 + x * 2ix2) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y Reorder the terms: (-4 + -8i + 4x + 8i + -8ix + 16i2 + (-2ix2 + 2ix3 + -4i2x2) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + 8i + -8ix + 16i2 + (-2ix2 + 2ix3 + -4i2x2) + -4x * (-1 + -2i + x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + (-1 * -4x + -2i * -4x + x * -4x) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y Reorder the terms: (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + (8ix + 4x + -4x2) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + (8ix + 4x + -4x2) + -1x2 * (-1 + -2i + x) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + 8ix + 4x + -4x2 + (-1 * -1x2 + -2i * -1x2 + x * -1x2) + x3(-1 + -2i + x)) = y Reorder the terms: (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + 8ix + 4x + -4x2 + (2ix2 + 1x2 + -1x3) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + 8ix + 4x + -4x2 + (2ix2 + 1x2 + -1x3) + x3(-1 + -2i + x)) = y (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + 8ix + 4x + -4x2 + 2ix2 + 1x2 + -1x3 + (-1 * x3 + -2i * x3 + x * x3)) = y Reorder the terms: (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + 8ix + 4x + -4x2 + 2ix2 + 1x2 + -1x3 + (-2ix3 + -1x3 + x4)) = y (-4 + -8i + 4x + 8i + -8ix + 16i2 + -2ix2 + 2ix3 + -4i2x2 + 8ix + 4x + -4x2 + 2ix2 + 1x2 + -1x3 + (-2ix3 + -1x3 + x4)) = y Reorder the terms: (-4 + -8i + 8i + -8ix + 8ix + -2ix2 + 2ix2 + 2ix3 + -2ix3 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y Combine like terms: -8i + 8i = 0 (-4 + 0 + -8ix + 8ix + -2ix2 + 2ix2 + 2ix3 + -2ix3 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y (-4 + -8ix + 8ix + -2ix2 + 2ix2 + 2ix3 + -2ix3 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y Combine like terms: -8ix + 8ix = 0 (-4 + 0 + -2ix2 + 2ix2 + 2ix3 + -2ix3 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y (-4 + -2ix2 + 2ix2 + 2ix3 + -2ix3 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y Combine like terms: -2ix2 + 2ix2 = 0 (-4 + 0 + 2ix3 + -2ix3 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y (-4 + 2ix3 + -2ix3 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y Combine like terms: 2ix3 + -2ix3 = 0 (-4 + 0 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y (-4 + 16i2 + -4i2x2 + 4x + 4x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y Combine like terms: 4x + 4x = 8x (-4 + 16i2 + -4i2x2 + 8x + -4x2 + 1x2 + -1x3 + -1x3 + x4) = y Combine like terms: -4x2 + 1x2 = -3x2 (-4 + 16i2 + -4i2x2 + 8x + -3x2 + -1x3 + -1x3 + x4) = y Combine like terms: -1x3 + -1x3 = -2x3 (-4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4) = y Solving -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 = y Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + 4 + x4 = 4 + y Reorder the terms: -4 + 4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 = 4 + y Combine like terms: -4 + 4 = 0 0 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 = 4 + y 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 = 4 + y Add '-8x' to each side of the equation. 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + -8x + x4 = 4 + -8x + y Reorder the terms: 16i2 + -4i2x2 + 8x + -8x + -3x2 + -2x3 + x4 = 4 + -8x + y Combine like terms: 8x + -8x = 0 16i2 + -4i2x2 + 0 + -3x2 + -2x3 + x4 = 4 + -8x + y 16i2 + -4i2x2 + -3x2 + -2x3 + x4 = 4 + -8x + y Add '3x2' to each side of the equation. 16i2 + -4i2x2 + -3x2 + -2x3 + 3x2 + x4 = 4 + -8x + 3x2 + y Reorder the terms: 16i2 + -4i2x2 + -3x2 + 3x2 + -2x3 + x4 = 4 + -8x + 3x2 + y Combine like terms: -3x2 + 3x2 = 0 16i2 + -4i2x2 + 0 + -2x3 + x4 = 4 + -8x + 3x2 + y 16i2 + -4i2x2 + -2x3 + x4 = 4 + -8x + 3x2 + y Add '2x3' to each side of the equation. 16i2 + -4i2x2 + -2x3 + 2x3 + x4 = 4 + -8x + 3x2 + 2x3 + y Combine like terms: -2x3 + 2x3 = 0 16i2 + -4i2x2 + 0 + x4 = 4 + -8x + 3x2 + 2x3 + y 16i2 + -4i2x2 + x4 = 4 + -8x + 3x2 + 2x3 + y Add '-1x4' to each side of the equation. 16i2 + -4i2x2 + x4 + -1x4 = 4 + -8x + 3x2 + 2x3 + -1x4 + y Combine like terms: x4 + -1x4 = 0 16i2 + -4i2x2 + 0 = 4 + -8x + 3x2 + 2x3 + -1x4 + y 16i2 + -4i2x2 = 4 + -8x + 3x2 + 2x3 + -1x4 + y Reorder the terms: -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 4 + -8x + 3x2 + 2x3 + -1x4 + y + -4 + 8x + -3x2 + -2x3 + x4 + -1y Reorder the terms: -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 4 + -4 + -8x + 8x + 3x2 + -3x2 + 2x3 + -2x3 + -1x4 + x4 + y + -1y Combine like terms: 4 + -4 = 0 -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 0 + -8x + 8x + 3x2 + -3x2 + 2x3 + -2x3 + -1x4 + x4 + y + -1y -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = -8x + 8x + 3x2 + -3x2 + 2x3 + -2x3 + -1x4 + x4 + y + -1y Combine like terms: -8x + 8x = 0 -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 0 + 3x2 + -3x2 + 2x3 + -2x3 + -1x4 + x4 + y + -1y -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 3x2 + -3x2 + 2x3 + -2x3 + -1x4 + x4 + y + -1y Combine like terms: 3x2 + -3x2 = 0 -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 0 + 2x3 + -2x3 + -1x4 + x4 + y + -1y -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 2x3 + -2x3 + -1x4 + x4 + y + -1y Combine like terms: 2x3 + -2x3 = 0 -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 0 + -1x4 + x4 + y + -1y -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = -1x4 + x4 + y + -1y Combine like terms: -1x4 + x4 = 0 -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 0 + y + -1y -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = y + -1y Combine like terms: y + -1y = 0 -4 + 16i2 + -4i2x2 + 8x + -3x2 + -2x3 + x4 + -1y = 0 The solution to this equation could not be determined.
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