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Simplifying (x + -1)(x + -3 + i)(x + -3 + -1i) = 0 Reorder the terms: (-1 + x)(x + -3 + i)(x + -3 + -1i) = 0 Reorder the terms: (-1 + x)(-3 + i + x)(x + -3 + -1i) = 0 Reorder the terms: (-1 + x)(-3 + i + x)(-3 + -1i + x) = 0 Multiply (-1 + x) * (-3 + i + x) (-1(-3 + i + x) + x(-3 + i + x))(-3 + -1i + x) = 0 ((-3 * -1 + i * -1 + x * -1) + x(-3 + i + x))(-3 + -1i + x) = 0 ((3 + -1i + -1x) + x(-3 + i + x))(-3 + -1i + x) = 0 (3 + -1i + -1x + (-3 * x + i * x + x * x))(-3 + -1i + x) = 0 Reorder the terms: (3 + -1i + -1x + (ix + -3x + x2))(-3 + -1i + x) = 0 (3 + -1i + -1x + (ix + -3x + x2))(-3 + -1i + x) = 0 Reorder the terms: (3 + -1i + ix + -1x + -3x + x2)(-3 + -1i + x) = 0 Combine like terms: -1x + -3x = -4x (3 + -1i + ix + -4x + x2)(-3 + -1i + x) = 0 Multiply (3 + -1i + ix + -4x + x2) * (-3 + -1i + x) (3(-3 + -1i + x) + -1i * (-3 + -1i + x) + ix(-3 + -1i + x) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 ((-3 * 3 + -1i * 3 + x * 3) + -1i * (-3 + -1i + x) + ix(-3 + -1i + x) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 ((-9 + -3i + 3x) + -1i * (-3 + -1i + x) + ix(-3 + -1i + x) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-9 + -3i + 3x + (-3 * -1i + -1i * -1i + x * -1i) + ix(-3 + -1i + x) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (-9 + -3i + 3x + (3i + -1ix + 1i2) + ix(-3 + -1i + x) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-9 + -3i + 3x + (3i + -1ix + 1i2) + ix(-3 + -1i + x) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-9 + -3i + 3x + 3i + -1ix + 1i2 + (-3 * ix + -1i * ix + x * ix) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (-9 + -3i + 3x + 3i + -1ix + 1i2 + (-3ix + ix2 + -1i2x) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-9 + -3i + 3x + 3i + -1ix + 1i2 + (-3ix + ix2 + -1i2x) + -4x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-9 + -3i + 3x + 3i + -1ix + 1i2 + -3ix + ix2 + -1i2x + (-3 * -4x + -1i * -4x + x * -4x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (-9 + -3i + 3x + 3i + -1ix + 1i2 + -3ix + ix2 + -1i2x + (4ix + 12x + -4x2) + x2(-3 + -1i + x)) = 0 (-9 + -3i + 3x + 3i + -1ix + 1i2 + -3ix + ix2 + -1i2x + (4ix + 12x + -4x2) + x2(-3 + -1i + x)) = 0 (-9 + -3i + 3x + 3i + -1ix + 1i2 + -3ix + ix2 + -1i2x + 4ix + 12x + -4x2 + (-3 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-9 + -3i + 3x + 3i + -1ix + 1i2 + -3ix + ix2 + -1i2x + 4ix + 12x + -4x2 + (-1ix2 + -3x2 + x3)) = 0 (-9 + -3i + 3x + 3i + -1ix + 1i2 + -3ix + ix2 + -1i2x + 4ix + 12x + -4x2 + (-1ix2 + -3x2 + x3)) = 0 Reorder the terms: (-9 + -3i + 3i + -1ix + -3ix + 4ix + ix2 + -1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0 Combine like terms: -3i + 3i = 0 (-9 + 0 + -1ix + -3ix + 4ix + ix2 + -1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0 (-9 + -1ix + -3ix + 4ix + ix2 + -1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0 Combine like terms: -1ix + -3ix = -4ix (-9 + -4ix + 4ix + ix2 + -1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0 Combine like terms: -4ix + 4ix = 0 (-9 + 0 + ix2 + -1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0 (-9 + ix2 + -1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (-9 + 0 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0 (-9 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0 Combine like terms: 3x + 12x = 15x (-9 + 1i2 + -1i2x + 15x + -4x2 + -3x2 + x3) = 0 Combine like terms: -4x2 + -3x2 = -7x2 (-9 + 1i2 + -1i2x + 15x + -7x2 + x3) = 0 Solving -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 1i2 + -1i2x + 15x + -7x2 + 9 + x3 = 0 + 9 Reorder the terms: -9 + 9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + 9 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + 9 Combine like terms: 0 + 9 = 9 1i2 + -1i2x + 15x + -7x2 + x3 = 9 Add '-15x' to each side of the equation. 1i2 + -1i2x + 15x + -7x2 + -15x + x3 = 9 + -15x Reorder the terms: 1i2 + -1i2x + 15x + -15x + -7x2 + x3 = 9 + -15x Combine like terms: 15x + -15x = 0 1i2 + -1i2x + 0 + -7x2 + x3 = 9 + -15x 1i2 + -1i2x + -7x2 + x3 = 9 + -15x Add '7x2' to each side of the equation. 1i2 + -1i2x + -7x2 + 7x2 + x3 = 9 + -15x + 7x2 Combine like terms: -7x2 + 7x2 = 0 1i2 + -1i2x + 0 + x3 = 9 + -15x + 7x2 1i2 + -1i2x + x3 = 9 + -15x + 7x2 Add '-1x3' to each side of the equation. 1i2 + -1i2x + x3 + -1x3 = 9 + -15x + 7x2 + -1x3 Combine like terms: x3 + -1x3 = 0 1i2 + -1i2x + 0 = 9 + -15x + 7x2 + -1x3 1i2 + -1i2x = 9 + -15x + 7x2 + -1x3 Reorder the terms: -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 9 + -15x + 7x2 + -1x3 + -9 + 15x + -7x2 + x3 Reorder the terms: -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 9 + -9 + -15x + 15x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: 9 + -9 = 0 -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + -15x + 15x + 7x2 + -7x2 + -1x3 + x3 -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = -15x + 15x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: -15x + 15x = 0 -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + 7x2 + -7x2 + -1x3 + x3 -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 7x2 + -7x2 + -1x3 + x3 Combine like terms: 7x2 + -7x2 = 0 -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + -1x3 + x3 -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 The solution to this equation could not be determined.
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