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Simplifying (x + -1(4 + -3i))(x + (4 + -3i))(x + -5)(x + -5) = 0 (x + (4 * -1 + -3i * -1))(x + (4 + -3i))(x + -5)(x + -5) = 0 (x + (-4 + 3i))(x + (4 + -3i))(x + -5)(x + -5) = 0 Reorder the terms: (-4 + 3i + x)(x + (4 + -3i))(x + -5)(x + -5) = 0 Remove parenthesis around (4 + -3i) (-4 + 3i + x)(x + 4 + -3i)(x + -5)(x + -5) = 0 Reorder the terms: (-4 + 3i + x)(4 + -3i + x)(x + -5)(x + -5) = 0 Reorder the terms: (-4 + 3i + x)(4 + -3i + x)(-5 + x)(x + -5) = 0 Reorder the terms: (-4 + 3i + x)(4 + -3i + x)(-5 + x)(-5 + x) = 0 Multiply (-4 + 3i + x) * (4 + -3i + x) (-4(4 + -3i + x) + 3i * (4 + -3i + x) + x(4 + -3i + x))(-5 + x)(-5 + x) = 0 ((4 * -4 + -3i * -4 + x * -4) + 3i * (4 + -3i + x) + x(4 + -3i + x))(-5 + x)(-5 + x) = 0 ((-16 + 12i + -4x) + 3i * (4 + -3i + x) + x(4 + -3i + x))(-5 + x)(-5 + x) = 0 (-16 + 12i + -4x + (4 * 3i + -3i * 3i + x * 3i) + x(4 + -3i + x))(-5 + x)(-5 + x) = 0 Reorder the terms: (-16 + 12i + -4x + (12i + 3ix + -9i2) + x(4 + -3i + x))(-5 + x)(-5 + x) = 0 (-16 + 12i + -4x + (12i + 3ix + -9i2) + x(4 + -3i + x))(-5 + x)(-5 + x) = 0 (-16 + 12i + -4x + 12i + 3ix + -9i2 + (4 * x + -3i * x + x * x))(-5 + x)(-5 + x) = 0 Reorder the terms: (-16 + 12i + -4x + 12i + 3ix + -9i2 + (-3ix + 4x + x2))(-5 + x)(-5 + x) = 0 (-16 + 12i + -4x + 12i + 3ix + -9i2 + (-3ix + 4x + x2))(-5 + x)(-5 + x) = 0 Reorder the terms: (-16 + 12i + 12i + 3ix + -3ix + -9i2 + -4x + 4x + x2)(-5 + x)(-5 + x) = 0 Combine like terms: 12i + 12i = 24i (-16 + 24i + 3ix + -3ix + -9i2 + -4x + 4x + x2)(-5 + x)(-5 + x) = 0 Combine like terms: 3ix + -3ix = 0 (-16 + 24i + 0 + -9i2 + -4x + 4x + x2)(-5 + x)(-5 + x) = 0 (-16 + 24i + -9i2 + -4x + 4x + x2)(-5 + x)(-5 + x) = 0 Combine like terms: -4x + 4x = 0 (-16 + 24i + -9i2 + 0 + x2)(-5 + x)(-5 + x) = 0 (-16 + 24i + -9i2 + x2)(-5 + x)(-5 + x) = 0 Multiply (-16 + 24i + -9i2 + x2) * (-5 + x) (-16(-5 + x) + 24i * (-5 + x) + -9i2 * (-5 + x) + x2(-5 + x))(-5 + x) = 0 ((-5 * -16 + x * -16) + 24i * (-5 + x) + -9i2 * (-5 + x) + x2(-5 + x))(-5 + x) = 0 ((80 + -16x) + 24i * (-5 + x) + -9i2 * (-5 + x) + x2(-5 + x))(-5 + x) = 0 (80 + -16x + (-5 * 24i + x * 24i) + -9i2 * (-5 + x) + x2(-5 + x))(-5 + x) = 0 (80 + -16x + (-120i + 24ix) + -9i2 * (-5 + x) + x2(-5 + x))(-5 + x) = 0 (80 + -16x + -120i + 24ix + (-5 * -9i2 + x * -9i2) + x2(-5 + x))(-5 + x) = 0 (80 + -16x + -120i + 24ix + (45i2 + -9i2x) + x2(-5 + x))(-5 + x) = 0 (80 + -16x + -120i + 24ix + 45i2 + -9i2x + (-5 * x2 + x * x2))(-5 + x) = 0 (80 + -16x + -120i + 24ix + 45i2 + -9i2x + (-5x2 + x3))(-5 + x) = 0 Reorder the terms: (80 + -120i + 24ix + 45i2 + -9i2x + -16x + -5x2 + x3)(-5 + x) = 0 (80 + -120i + 24ix + 45i2 + -9i2x + -16x + -5x2 + x3)(-5 + x) = 0 Multiply (80 + -120i + 24ix + 45i2 + -9i2x + -16x + -5x2 + x3) * (-5 + x) (80(-5 + x) + -120i * (-5 + x) + 24ix * (-5 + x) + 45i2 * (-5 + x) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 ((-5 * 80 + x * 80) + -120i * (-5 + x) + 24ix * (-5 + x) + 45i2 * (-5 + x) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 ((-400 + 80x) + -120i * (-5 + x) + 24ix * (-5 + x) + 45i2 * (-5 + x) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + (-5 * -120i + x * -120i) + 24ix * (-5 + x) + 45i2 * (-5 + x) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + (600i + -120ix) + 24ix * (-5 + x) + 45i2 * (-5 + x) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + (-5 * 24ix + x * 24ix) + 45i2 * (-5 + x) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + (-120ix + 24ix2) + 45i2 * (-5 + x) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + (-5 * 45i2 + x * 45i2) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + (-225i2 + 45i2x) + -9i2x * (-5 + x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + (-5 * -9i2x + x * -9i2x) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + (45i2x + -9i2x2) + -16x * (-5 + x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + 45i2x + -9i2x2 + (-5 * -16x + x * -16x) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + 45i2x + -9i2x2 + (80x + -16x2) + -5x2 * (-5 + x) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + 45i2x + -9i2x2 + 80x + -16x2 + (-5 * -5x2 + x * -5x2) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + 45i2x + -9i2x2 + 80x + -16x2 + (25x2 + -5x3) + x3(-5 + x)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + 45i2x + -9i2x2 + 80x + -16x2 + 25x2 + -5x3 + (-5 * x3 + x * x3)) = 0 (-400 + 80x + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + 45i2x + -9i2x2 + 80x + -16x2 + 25x2 + -5x3 + (-5x3 + x4)) = 0 Reorder the terms: (-400 + 600i + -120ix + -120ix + 24ix2 + -225i2 + 45i2x + 45i2x + -9i2x2 + 80x + 80x + -16x2 + 25x2 + -5x3 + -5x3 + x4) = 0 Combine like terms: -120ix + -120ix = -240ix (-400 + 600i + -240ix + 24ix2 + -225i2 + 45i2x + 45i2x + -9i2x2 + 80x + 80x + -16x2 + 25x2 + -5x3 + -5x3 + x4) = 0 Combine like terms: 45i2x + 45i2x = 90i2x (-400 + 600i + -240ix + 24ix2 + -225i2 + 90i2x + -9i2x2 + 80x + 80x + -16x2 + 25x2 + -5x3 + -5x3 + x4) = 0 Combine like terms: 80x + 80x = 160x (-400 + 600i + -240ix + 24ix2 + -225i2 + 90i2x + -9i2x2 + 160x + -16x2 + 25x2 + -5x3 + -5x3 + x4) = 0 Combine like terms: -16x2 + 25x2 = 9x2 (-400 + 600i + -240ix + 24ix2 + -225i2 + 90i2x + -9i2x2 + 160x + 9x2 + -5x3 + -5x3 + x4) = 0 Combine like terms: -5x3 + -5x3 = -10x3 (-400 + 600i + -240ix + 24ix2 + -225i2 + 90i2x + -9i2x2 + 160x + 9x2 + -10x3 + x4) = 0 Solving -400 + 600i + -240ix + 24ix2 + -225i2 + 90i2x + -9i2x2 + 160x + 9x2 + -10x3 + x4 = 0 Solving for variable 'i'. The solution to this equation could not be determined.
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