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Simplifying (x + 1)(x + -2)(x + 3i) = 0 Reorder the terms: (1 + x)(x + -2)(x + 3i) = 0 Reorder the terms: (1 + x)(-2 + x)(x + 3i) = 0 Reorder the terms: (1 + x)(-2 + x)(3i + x) = 0 Multiply (1 + x) * (-2 + x) (1(-2 + x) + x(-2 + x))(3i + x) = 0 ((-2 * 1 + x * 1) + x(-2 + x))(3i + x) = 0 ((-2 + 1x) + x(-2 + x))(3i + x) = 0 (-2 + 1x + (-2 * x + x * x))(3i + x) = 0 (-2 + 1x + (-2x + x2))(3i + x) = 0 Combine like terms: 1x + -2x = -1x (-2 + -1x + x2)(3i + x) = 0 Multiply (-2 + -1x + x2) * (3i + x) (-2(3i + x) + -1x * (3i + x) + x2(3i + x)) = 0 ((3i * -2 + x * -2) + -1x * (3i + x) + x2(3i + x)) = 0 ((-6i + -2x) + -1x * (3i + x) + x2(3i + x)) = 0 (-6i + -2x + (3i * -1x + x * -1x) + x2(3i + x)) = 0 (-6i + -2x + (-3ix + -1x2) + x2(3i + x)) = 0 (-6i + -2x + -3ix + -1x2 + (3i * x2 + x * x2)) = 0 (-6i + -2x + -3ix + -1x2 + (3ix2 + x3)) = 0 Reorder the terms: (-6i + -3ix + 3ix2 + -2x + -1x2 + x3) = 0 (-6i + -3ix + 3ix2 + -2x + -1x2 + x3) = 0 Solving -6i + -3ix + 3ix2 + -2x + -1x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2x' to each side of the equation. -6i + -3ix + 3ix2 + -2x + -1x2 + 2x + x3 = 0 + 2x Reorder the terms: -6i + -3ix + 3ix2 + -2x + 2x + -1x2 + x3 = 0 + 2x Combine like terms: -2x + 2x = 0 -6i + -3ix + 3ix2 + 0 + -1x2 + x3 = 0 + 2x -6i + -3ix + 3ix2 + -1x2 + x3 = 0 + 2x Remove the zero: -6i + -3ix + 3ix2 + -1x2 + x3 = 2x Add 'x2' to each side of the equation. -6i + -3ix + 3ix2 + -1x2 + x2 + x3 = 2x + x2 Combine like terms: -1x2 + x2 = 0 -6i + -3ix + 3ix2 + 0 + x3 = 2x + x2 -6i + -3ix + 3ix2 + x3 = 2x + x2 Add '-1x3' to each side of the equation. -6i + -3ix + 3ix2 + x3 + -1x3 = 2x + x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -6i + -3ix + 3ix2 + 0 = 2x + x2 + -1x3 -6i + -3ix + 3ix2 = 2x + x2 + -1x3 Reorder the terms: -6i + -3ix + 3ix2 + -2x + -1x2 + x3 = 2x + -2x + x2 + -1x2 + -1x3 + x3 Combine like terms: 2x + -2x = 0 -6i + -3ix + 3ix2 + -2x + -1x2 + x3 = 0 + x2 + -1x2 + -1x3 + x3 -6i + -3ix + 3ix2 + -2x + -1x2 + x3 = x2 + -1x2 + -1x3 + x3 Combine like terms: x2 + -1x2 = 0 -6i + -3ix + 3ix2 + -2x + -1x2 + x3 = 0 + -1x3 + x3 -6i + -3ix + 3ix2 + -2x + -1x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -6i + -3ix + 3ix2 + -2x + -1x2 + x3 = 0 The solution to this equation could not be determined.
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