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Simplifying (x + -2 + -3i)(x + 1)(x + -2) = 0 Reorder the terms: (-2 + -3i + x)(x + 1)(x + -2) = 0 Reorder the terms: (-2 + -3i + x)(1 + x)(x + -2) = 0 Reorder the terms: (-2 + -3i + x)(1 + x)(-2 + x) = 0 Multiply (-2 + -3i + x) * (1 + x) (-2(1 + x) + -3i * (1 + x) + x(1 + x))(-2 + x) = 0 ((1 * -2 + x * -2) + -3i * (1 + x) + x(1 + x))(-2 + x) = 0 ((-2 + -2x) + -3i * (1 + x) + x(1 + x))(-2 + x) = 0 (-2 + -2x + (1 * -3i + x * -3i) + x(1 + x))(-2 + x) = 0 (-2 + -2x + (-3i + -3ix) + x(1 + x))(-2 + x) = 0 (-2 + -2x + -3i + -3ix + (1 * x + x * x))(-2 + x) = 0 (-2 + -2x + -3i + -3ix + (1x + x2))(-2 + x) = 0 Reorder the terms: (-2 + -3i + -3ix + -2x + 1x + x2)(-2 + x) = 0 Combine like terms: -2x + 1x = -1x (-2 + -3i + -3ix + -1x + x2)(-2 + x) = 0 Multiply (-2 + -3i + -3ix + -1x + x2) * (-2 + x) (-2(-2 + x) + -3i * (-2 + x) + -3ix * (-2 + x) + -1x * (-2 + x) + x2(-2 + x)) = 0 ((-2 * -2 + x * -2) + -3i * (-2 + x) + -3ix * (-2 + x) + -1x * (-2 + x) + x2(-2 + x)) = 0 ((4 + -2x) + -3i * (-2 + x) + -3ix * (-2 + x) + -1x * (-2 + x) + x2(-2 + x)) = 0 (4 + -2x + (-2 * -3i + x * -3i) + -3ix * (-2 + x) + -1x * (-2 + x) + x2(-2 + x)) = 0 (4 + -2x + (6i + -3ix) + -3ix * (-2 + x) + -1x * (-2 + x) + x2(-2 + x)) = 0 (4 + -2x + 6i + -3ix + (-2 * -3ix + x * -3ix) + -1x * (-2 + x) + x2(-2 + x)) = 0 (4 + -2x + 6i + -3ix + (6ix + -3ix2) + -1x * (-2 + x) + x2(-2 + x)) = 0 (4 + -2x + 6i + -3ix + 6ix + -3ix2 + (-2 * -1x + x * -1x) + x2(-2 + x)) = 0 (4 + -2x + 6i + -3ix + 6ix + -3ix2 + (2x + -1x2) + x2(-2 + x)) = 0 (4 + -2x + 6i + -3ix + 6ix + -3ix2 + 2x + -1x2 + (-2 * x2 + x * x2)) = 0 (4 + -2x + 6i + -3ix + 6ix + -3ix2 + 2x + -1x2 + (-2x2 + x3)) = 0 Reorder the terms: (4 + 6i + -3ix + 6ix + -3ix2 + -2x + 2x + -1x2 + -2x2 + x3) = 0 Combine like terms: -3ix + 6ix = 3ix (4 + 6i + 3ix + -3ix2 + -2x + 2x + -1x2 + -2x2 + x3) = 0 Combine like terms: -2x + 2x = 0 (4 + 6i + 3ix + -3ix2 + 0 + -1x2 + -2x2 + x3) = 0 (4 + 6i + 3ix + -3ix2 + -1x2 + -2x2 + x3) = 0 Combine like terms: -1x2 + -2x2 = -3x2 (4 + 6i + 3ix + -3ix2 + -3x2 + x3) = 0 Solving 4 + 6i + 3ix + -3ix2 + -3x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 6i + 3ix + -3ix2 + -3x2 + -4 + x3 = 0 + -4 Reorder the terms: 4 + -4 + 6i + 3ix + -3ix2 + -3x2 + x3 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6i + 3ix + -3ix2 + -3x2 + x3 = 0 + -4 6i + 3ix + -3ix2 + -3x2 + x3 = 0 + -4 Combine like terms: 0 + -4 = -4 6i + 3ix + -3ix2 + -3x2 + x3 = -4 Add '3x2' to each side of the equation. 6i + 3ix + -3ix2 + -3x2 + 3x2 + x3 = -4 + 3x2 Combine like terms: -3x2 + 3x2 = 0 6i + 3ix + -3ix2 + 0 + x3 = -4 + 3x2 6i + 3ix + -3ix2 + x3 = -4 + 3x2 Add '-1x3' to each side of the equation. 6i + 3ix + -3ix2 + x3 + -1x3 = -4 + 3x2 + -1x3 Combine like terms: x3 + -1x3 = 0 6i + 3ix + -3ix2 + 0 = -4 + 3x2 + -1x3 6i + 3ix + -3ix2 = -4 + 3x2 + -1x3 Reorder the terms: 4 + 6i + 3ix + -3ix2 + -3x2 + x3 = -4 + 3x2 + -1x3 + 4 + -3x2 + x3 Reorder the terms: 4 + 6i + 3ix + -3ix2 + -3x2 + x3 = -4 + 4 + 3x2 + -3x2 + -1x3 + x3 Combine like terms: -4 + 4 = 0 4 + 6i + 3ix + -3ix2 + -3x2 + x3 = 0 + 3x2 + -3x2 + -1x3 + x3 4 + 6i + 3ix + -3ix2 + -3x2 + x3 = 3x2 + -3x2 + -1x3 + x3 Combine like terms: 3x2 + -3x2 = 0 4 + 6i + 3ix + -3ix2 + -3x2 + x3 = 0 + -1x3 + x3 4 + 6i + 3ix + -3ix2 + -3x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 4 + 6i + 3ix + -3ix2 + -3x2 + x3 = 0 The solution to this equation could not be determined.
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