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Simplifying (x + 4 + -1i)(x + 4 + i)(x + 5) = 0 Reorder the terms: (4 + -1i + x)(x + 4 + i)(x + 5) = 0 Reorder the terms: (4 + -1i + x)(4 + i + x)(x + 5) = 0 Reorder the terms: (4 + -1i + x)(4 + i + x)(5 + x) = 0 Multiply (4 + -1i + x) * (4 + i + x) (4(4 + i + x) + -1i * (4 + i + x) + x(4 + i + x))(5 + x) = 0 ((4 * 4 + i * 4 + x * 4) + -1i * (4 + i + x) + x(4 + i + x))(5 + x) = 0 ((16 + 4i + 4x) + -1i * (4 + i + x) + x(4 + i + x))(5 + x) = 0 (16 + 4i + 4x + (4 * -1i + i * -1i + x * -1i) + x(4 + i + x))(5 + x) = 0 Reorder the terms: (16 + 4i + 4x + (-4i + -1ix + -1i2) + x(4 + i + x))(5 + x) = 0 (16 + 4i + 4x + (-4i + -1ix + -1i2) + x(4 + i + x))(5 + x) = 0 (16 + 4i + 4x + -4i + -1ix + -1i2 + (4 * x + i * x + x * x))(5 + x) = 0 Reorder the terms: (16 + 4i + 4x + -4i + -1ix + -1i2 + (ix + 4x + x2))(5 + x) = 0 (16 + 4i + 4x + -4i + -1ix + -1i2 + (ix + 4x + x2))(5 + x) = 0 Reorder the terms: (16 + 4i + -4i + -1ix + ix + -1i2 + 4x + 4x + x2)(5 + x) = 0 Combine like terms: 4i + -4i = 0 (16 + 0 + -1ix + ix + -1i2 + 4x + 4x + x2)(5 + x) = 0 (16 + -1ix + ix + -1i2 + 4x + 4x + x2)(5 + x) = 0 Combine like terms: -1ix + ix = 0 (16 + 0 + -1i2 + 4x + 4x + x2)(5 + x) = 0 (16 + -1i2 + 4x + 4x + x2)(5 + x) = 0 Combine like terms: 4x + 4x = 8x (16 + -1i2 + 8x + x2)(5 + x) = 0 Multiply (16 + -1i2 + 8x + x2) * (5 + x) (16(5 + x) + -1i2 * (5 + x) + 8x * (5 + x) + x2(5 + x)) = 0 ((5 * 16 + x * 16) + -1i2 * (5 + x) + 8x * (5 + x) + x2(5 + x)) = 0 ((80 + 16x) + -1i2 * (5 + x) + 8x * (5 + x) + x2(5 + x)) = 0 (80 + 16x + (5 * -1i2 + x * -1i2) + 8x * (5 + x) + x2(5 + x)) = 0 (80 + 16x + (-5i2 + -1i2x) + 8x * (5 + x) + x2(5 + x)) = 0 (80 + 16x + -5i2 + -1i2x + (5 * 8x + x * 8x) + x2(5 + x)) = 0 (80 + 16x + -5i2 + -1i2x + (40x + 8x2) + x2(5 + x)) = 0 (80 + 16x + -5i2 + -1i2x + 40x + 8x2 + (5 * x2 + x * x2)) = 0 (80 + 16x + -5i2 + -1i2x + 40x + 8x2 + (5x2 + x3)) = 0 Reorder the terms: (80 + -5i2 + -1i2x + 16x + 40x + 8x2 + 5x2 + x3) = 0 Combine like terms: 16x + 40x = 56x (80 + -5i2 + -1i2x + 56x + 8x2 + 5x2 + x3) = 0 Combine like terms: 8x2 + 5x2 = 13x2 (80 + -5i2 + -1i2x + 56x + 13x2 + x3) = 0 Solving 80 + -5i2 + -1i2x + 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 + -5i2 + -1i2x + 56x + 13x2 + -80 + x3 = 0 + -80 Reorder the terms: 80 + -80 + -5i2 + -1i2x + 56x + 13x2 + x3 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -5i2 + -1i2x + 56x + 13x2 + x3 = 0 + -80 -5i2 + -1i2x + 56x + 13x2 + x3 = 0 + -80 Combine like terms: 0 + -80 = -80 -5i2 + -1i2x + 56x + 13x2 + x3 = -80 Add '-56x' to each side of the equation. -5i2 + -1i2x + 56x + 13x2 + -56x + x3 = -80 + -56x Reorder the terms: -5i2 + -1i2x + 56x + -56x + 13x2 + x3 = -80 + -56x Combine like terms: 56x + -56x = 0 -5i2 + -1i2x + 0 + 13x2 + x3 = -80 + -56x -5i2 + -1i2x + 13x2 + x3 = -80 + -56x Add '-13x2' to each side of the equation. -5i2 + -1i2x + 13x2 + -13x2 + x3 = -80 + -56x + -13x2 Combine like terms: 13x2 + -13x2 = 0 -5i2 + -1i2x + 0 + x3 = -80 + -56x + -13x2 -5i2 + -1i2x + x3 = -80 + -56x + -13x2 Add '-1x3' to each side of the equation. -5i2 + -1i2x + x3 + -1x3 = -80 + -56x + -13x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -5i2 + -1i2x + 0 = -80 + -56x + -13x2 + -1x3 -5i2 + -1i2x = -80 + -56x + -13x2 + -1x3 Reorder the terms: 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = -80 + -56x + -13x2 + -1x3 + 80 + 56x + 13x2 + x3 Reorder the terms: 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = -80 + 80 + -56x + 56x + -13x2 + 13x2 + -1x3 + x3 Combine like terms: -80 + 80 = 0 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = 0 + -56x + 56x + -13x2 + 13x2 + -1x3 + x3 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = -56x + 56x + -13x2 + 13x2 + -1x3 + x3 Combine like terms: -56x + 56x = 0 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = 0 + -13x2 + 13x2 + -1x3 + x3 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = -13x2 + 13x2 + -1x3 + x3 Combine like terms: -13x2 + 13x2 = 0 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = 0 + -1x3 + x3 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 80 + -5i2 + -1i2x + 56x + 13x2 + x3 = 0 The solution to this equation could not be determined.
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