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Simplifying (x + 3)(x + -1)(x + 3i) = 0 Reorder the terms: (3 + x)(x + -1)(x + 3i) = 0 Reorder the terms: (3 + x)(-1 + x)(x + 3i) = 0 Reorder the terms: (3 + x)(-1 + x)(3i + x) = 0 Multiply (3 + x) * (-1 + x) (3(-1 + x) + x(-1 + x))(3i + x) = 0 ((-1 * 3 + x * 3) + x(-1 + x))(3i + x) = 0 ((-3 + 3x) + x(-1 + x))(3i + x) = 0 (-3 + 3x + (-1 * x + x * x))(3i + x) = 0 (-3 + 3x + (-1x + x2))(3i + x) = 0 Combine like terms: 3x + -1x = 2x (-3 + 2x + x2)(3i + x) = 0 Multiply (-3 + 2x + x2) * (3i + x) (-3(3i + x) + 2x * (3i + x) + x2(3i + x)) = 0 ((3i * -3 + x * -3) + 2x * (3i + x) + x2(3i + x)) = 0 ((-9i + -3x) + 2x * (3i + x) + x2(3i + x)) = 0 (-9i + -3x + (3i * 2x + x * 2x) + x2(3i + x)) = 0 (-9i + -3x + (6ix + 2x2) + x2(3i + x)) = 0 (-9i + -3x + 6ix + 2x2 + (3i * x2 + x * x2)) = 0 (-9i + -3x + 6ix + 2x2 + (3ix2 + x3)) = 0 Reorder the terms: (-9i + 6ix + 3ix2 + -3x + 2x2 + x3) = 0 (-9i + 6ix + 3ix2 + -3x + 2x2 + x3) = 0 Solving -9i + 6ix + 3ix2 + -3x + 2x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3x' to each side of the equation. -9i + 6ix + 3ix2 + -3x + 2x2 + 3x + x3 = 0 + 3x Reorder the terms: -9i + 6ix + 3ix2 + -3x + 3x + 2x2 + x3 = 0 + 3x Combine like terms: -3x + 3x = 0 -9i + 6ix + 3ix2 + 0 + 2x2 + x3 = 0 + 3x -9i + 6ix + 3ix2 + 2x2 + x3 = 0 + 3x Remove the zero: -9i + 6ix + 3ix2 + 2x2 + x3 = 3x Add '-2x2' to each side of the equation. -9i + 6ix + 3ix2 + 2x2 + -2x2 + x3 = 3x + -2x2 Combine like terms: 2x2 + -2x2 = 0 -9i + 6ix + 3ix2 + 0 + x3 = 3x + -2x2 -9i + 6ix + 3ix2 + x3 = 3x + -2x2 Add '-1x3' to each side of the equation. -9i + 6ix + 3ix2 + x3 + -1x3 = 3x + -2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -9i + 6ix + 3ix2 + 0 = 3x + -2x2 + -1x3 -9i + 6ix + 3ix2 = 3x + -2x2 + -1x3 Reorder the terms: -9i + 6ix + 3ix2 + -3x + 2x2 + x3 = 3x + -3x + -2x2 + 2x2 + -1x3 + x3 Combine like terms: 3x + -3x = 0 -9i + 6ix + 3ix2 + -3x + 2x2 + x3 = 0 + -2x2 + 2x2 + -1x3 + x3 -9i + 6ix + 3ix2 + -3x + 2x2 + x3 = -2x2 + 2x2 + -1x3 + x3 Combine like terms: -2x2 + 2x2 = 0 -9i + 6ix + 3ix2 + -3x + 2x2 + x3 = 0 + -1x3 + x3 -9i + 6ix + 3ix2 + -3x + 2x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -9i + 6ix + 3ix2 + -3x + 2x2 + x3 = 0 The solution to this equation could not be determined.
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