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Simplifying (x + 5)(x + 4 + 3i)(x + 4 + -3i) = 0 Reorder the terms: (5 + x)(x + 4 + 3i)(x + 4 + -3i) = 0 Reorder the terms: (5 + x)(4 + 3i + x)(x + 4 + -3i) = 0 Reorder the terms: (5 + x)(4 + 3i + x)(4 + -3i + x) = 0 Multiply (5 + x) * (4 + 3i + x) (5(4 + 3i + x) + x(4 + 3i + x))(4 + -3i + x) = 0 ((4 * 5 + 3i * 5 + x * 5) + x(4 + 3i + x))(4 + -3i + x) = 0 ((20 + 15i + 5x) + x(4 + 3i + x))(4 + -3i + x) = 0 (20 + 15i + 5x + (4 * x + 3i * x + x * x))(4 + -3i + x) = 0 Reorder the terms: (20 + 15i + 5x + (3ix + 4x + x2))(4 + -3i + x) = 0 (20 + 15i + 5x + (3ix + 4x + x2))(4 + -3i + x) = 0 Reorder the terms: (20 + 15i + 3ix + 5x + 4x + x2)(4 + -3i + x) = 0 Combine like terms: 5x + 4x = 9x (20 + 15i + 3ix + 9x + x2)(4 + -3i + x) = 0 Multiply (20 + 15i + 3ix + 9x + x2) * (4 + -3i + x) (20(4 + -3i + x) + 15i * (4 + -3i + x) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 ((4 * 20 + -3i * 20 + x * 20) + 15i * (4 + -3i + x) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 ((80 + -60i + 20x) + 15i * (4 + -3i + x) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 (80 + -60i + 20x + (4 * 15i + -3i * 15i + x * 15i) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 Reorder the terms: (80 + -60i + 20x + (60i + 15ix + -45i2) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 (80 + -60i + 20x + (60i + 15ix + -45i2) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 (80 + -60i + 20x + 60i + 15ix + -45i2 + (4 * 3ix + -3i * 3ix + x * 3ix) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 Reorder the terms: (80 + -60i + 20x + 60i + 15ix + -45i2 + (12ix + 3ix2 + -9i2x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 (80 + -60i + 20x + 60i + 15ix + -45i2 + (12ix + 3ix2 + -9i2x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0 (80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + (4 * 9x + -3i * 9x + x * 9x) + x2(4 + -3i + x)) = 0 Reorder the terms: (80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + (-27ix + 36x + 9x2) + x2(4 + -3i + x)) = 0 (80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + (-27ix + 36x + 9x2) + x2(4 + -3i + x)) = 0 (80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + -27ix + 36x + 9x2 + (4 * x2 + -3i * x2 + x * x2)) = 0 Reorder the terms: (80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + -27ix + 36x + 9x2 + (-3ix2 + 4x2 + x3)) = 0 (80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + -27ix + 36x + 9x2 + (-3ix2 + 4x2 + x3)) = 0 Reorder the terms: (80 + -60i + 60i + 15ix + 12ix + -27ix + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0 Combine like terms: -60i + 60i = 0 (80 + 0 + 15ix + 12ix + -27ix + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0 (80 + 15ix + 12ix + -27ix + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0 Combine like terms: 15ix + 12ix = 27ix (80 + 27ix + -27ix + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0 Combine like terms: 27ix + -27ix = 0 (80 + 0 + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0 (80 + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0 Combine like terms: 3ix2 + -3ix2 = 0 (80 + 0 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0 (80 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0 Combine like terms: 20x + 36x = 56x (80 + -45i2 + -9i2x + 56x + 9x2 + 4x2 + x3) = 0 Combine like terms: 9x2 + 4x2 = 13x2 (80 + -45i2 + -9i2x + 56x + 13x2 + x3) = 0 Solving 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -45i2 + -9i2x + 56x + 13x2 + -80 + x3 = 0 + -80 Reorder the terms: 80 + -80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -80 -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -80 Combine like terms: 0 + -80 = -80 -45i2 + -9i2x + 56x + 13x2 + x3 = -80 Add '-56x' to each side of the equation. -45i2 + -9i2x + 56x + 13x2 + -56x + x3 = -80 + -56x Reorder the terms: -45i2 + -9i2x + 56x + -56x + 13x2 + x3 = -80 + -56x Combine like terms: 56x + -56x = 0 -45i2 + -9i2x + 0 + 13x2 + x3 = -80 + -56x -45i2 + -9i2x + 13x2 + x3 = -80 + -56x Add '-13x2' to each side of the equation. -45i2 + -9i2x + 13x2 + -13x2 + x3 = -80 + -56x + -13x2 Combine like terms: 13x2 + -13x2 = 0 -45i2 + -9i2x + 0 + x3 = -80 + -56x + -13x2 -45i2 + -9i2x + x3 = -80 + -56x + -13x2 Add '-1x3' to each side of the equation. -45i2 + -9i2x + x3 + -1x3 = -80 + -56x + -13x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -45i2 + -9i2x + 0 = -80 + -56x + -13x2 + -1x3 -45i2 + -9i2x = -80 + -56x + -13x2 + -1x3 Reorder the terms: 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -80 + -56x + -13x2 + -1x3 + 80 + 56x + 13x2 + x3 Reorder the terms: 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -80 + 80 + -56x + 56x + -13x2 + 13x2 + -1x3 + x3 Combine like terms: -80 + 80 = 0 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -56x + 56x + -13x2 + 13x2 + -1x3 + x3 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -56x + 56x + -13x2 + 13x2 + -1x3 + x3 Combine like terms: -56x + 56x = 0 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -13x2 + 13x2 + -1x3 + x3 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -13x2 + 13x2 + -1x3 + x3 Combine like terms: -13x2 + 13x2 = 0 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -1x3 + x3 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 The solution to this equation could not be determined.
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