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Simplifying (x + 3 + -3i)(x + 3 + 3i)(x + 1)(x + -2) = 0 Reorder the terms: (3 + -3i + x)(x + 3 + 3i)(x + 1)(x + -2) = 0 Reorder the terms: (3 + -3i + x)(3 + 3i + x)(x + 1)(x + -2) = 0 Reorder the terms: (3 + -3i + x)(3 + 3i + x)(1 + x)(x + -2) = 0 Reorder the terms: (3 + -3i + x)(3 + 3i + x)(1 + x)(-2 + x) = 0 Multiply (3 + -3i + x) * (3 + 3i + x) (3(3 + 3i + x) + -3i * (3 + 3i + x) + x(3 + 3i + x))(1 + x)(-2 + x) = 0 ((3 * 3 + 3i * 3 + x * 3) + -3i * (3 + 3i + x) + x(3 + 3i + x))(1 + x)(-2 + x) = 0 ((9 + 9i + 3x) + -3i * (3 + 3i + x) + x(3 + 3i + x))(1 + x)(-2 + x) = 0 (9 + 9i + 3x + (3 * -3i + 3i * -3i + x * -3i) + x(3 + 3i + x))(1 + x)(-2 + x) = 0 Reorder the terms: (9 + 9i + 3x + (-9i + -3ix + -9i2) + x(3 + 3i + x))(1 + x)(-2 + x) = 0 (9 + 9i + 3x + (-9i + -3ix + -9i2) + x(3 + 3i + x))(1 + x)(-2 + x) = 0 (9 + 9i + 3x + -9i + -3ix + -9i2 + (3 * x + 3i * x + x * x))(1 + x)(-2 + x) = 0 Reorder the terms: (9 + 9i + 3x + -9i + -3ix + -9i2 + (3ix + 3x + x2))(1 + x)(-2 + x) = 0 (9 + 9i + 3x + -9i + -3ix + -9i2 + (3ix + 3x + x2))(1 + x)(-2 + x) = 0 Reorder the terms: (9 + 9i + -9i + -3ix + 3ix + -9i2 + 3x + 3x + x2)(1 + x)(-2 + x) = 0 Combine like terms: 9i + -9i = 0 (9 + 0 + -3ix + 3ix + -9i2 + 3x + 3x + x2)(1 + x)(-2 + x) = 0 (9 + -3ix + 3ix + -9i2 + 3x + 3x + x2)(1 + x)(-2 + x) = 0 Combine like terms: -3ix + 3ix = 0 (9 + 0 + -9i2 + 3x + 3x + x2)(1 + x)(-2 + x) = 0 (9 + -9i2 + 3x + 3x + x2)(1 + x)(-2 + x) = 0 Combine like terms: 3x + 3x = 6x (9 + -9i2 + 6x + x2)(1 + x)(-2 + x) = 0 Multiply (9 + -9i2 + 6x + x2) * (1 + x) (9(1 + x) + -9i2 * (1 + x) + 6x * (1 + x) + x2(1 + x))(-2 + x) = 0 ((1 * 9 + x * 9) + -9i2 * (1 + x) + 6x * (1 + x) + x2(1 + x))(-2 + x) = 0 ((9 + 9x) + -9i2 * (1 + x) + 6x * (1 + x) + x2(1 + x))(-2 + x) = 0 (9 + 9x + (1 * -9i2 + x * -9i2) + 6x * (1 + x) + x2(1 + x))(-2 + x) = 0 (9 + 9x + (-9i2 + -9i2x) + 6x * (1 + x) + x2(1 + x))(-2 + x) = 0 (9 + 9x + -9i2 + -9i2x + (1 * 6x + x * 6x) + x2(1 + x))(-2 + x) = 0 (9 + 9x + -9i2 + -9i2x + (6x + 6x2) + x2(1 + x))(-2 + x) = 0 (9 + 9x + -9i2 + -9i2x + 6x + 6x2 + (1 * x2 + x * x2))(-2 + x) = 0 (9 + 9x + -9i2 + -9i2x + 6x + 6x2 + (1x2 + x3))(-2 + x) = 0 Reorder the terms: (9 + -9i2 + -9i2x + 9x + 6x + 6x2 + 1x2 + x3)(-2 + x) = 0 Combine like terms: 9x + 6x = 15x (9 + -9i2 + -9i2x + 15x + 6x2 + 1x2 + x3)(-2 + x) = 0 Combine like terms: 6x2 + 1x2 = 7x2 (9 + -9i2 + -9i2x + 15x + 7x2 + x3)(-2 + x) = 0 Multiply (9 + -9i2 + -9i2x + 15x + 7x2 + x3) * (-2 + x) (9(-2 + x) + -9i2 * (-2 + x) + -9i2x * (-2 + x) + 15x * (-2 + x) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 ((-2 * 9 + x * 9) + -9i2 * (-2 + x) + -9i2x * (-2 + x) + 15x * (-2 + x) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 ((-18 + 9x) + -9i2 * (-2 + x) + -9i2x * (-2 + x) + 15x * (-2 + x) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 (-18 + 9x + (-2 * -9i2 + x * -9i2) + -9i2x * (-2 + x) + 15x * (-2 + x) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 (-18 + 9x + (18i2 + -9i2x) + -9i2x * (-2 + x) + 15x * (-2 + x) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 (-18 + 9x + 18i2 + -9i2x + (-2 * -9i2x + x * -9i2x) + 15x * (-2 + x) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 (-18 + 9x + 18i2 + -9i2x + (18i2x + -9i2x2) + 15x * (-2 + x) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 (-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + (-2 * 15x + x * 15x) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 (-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + (-30x + 15x2) + 7x2 * (-2 + x) + x3(-2 + x)) = 0 (-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + -30x + 15x2 + (-2 * 7x2 + x * 7x2) + x3(-2 + x)) = 0 (-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + -30x + 15x2 + (-14x2 + 7x3) + x3(-2 + x)) = 0 (-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + -30x + 15x2 + -14x2 + 7x3 + (-2 * x3 + x * x3)) = 0 (-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + -30x + 15x2 + -14x2 + 7x3 + (-2x3 + x4)) = 0 Reorder the terms: (-18 + 18i2 + -9i2x + 18i2x + -9i2x2 + 9x + -30x + 15x2 + -14x2 + 7x3 + -2x3 + x4) = 0 Combine like terms: -9i2x + 18i2x = 9i2x (-18 + 18i2 + 9i2x + -9i2x2 + 9x + -30x + 15x2 + -14x2 + 7x3 + -2x3 + x4) = 0 Combine like terms: 9x + -30x = -21x (-18 + 18i2 + 9i2x + -9i2x2 + -21x + 15x2 + -14x2 + 7x3 + -2x3 + x4) = 0 Combine like terms: 15x2 + -14x2 = 1x2 (-18 + 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 7x3 + -2x3 + x4) = 0 Combine like terms: 7x3 + -2x3 = 5x3 (-18 + 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 5x3 + x4) = 0 Solving -18 + 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 5x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 5x3 + 18 + x4 = 0 + 18 Reorder the terms: -18 + 18 + 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 5x3 + x4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 5x3 + x4 = 0 + 18 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 5x3 + x4 = 0 + 18 Combine like terms: 0 + 18 = 18 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 5x3 + x4 = 18 Add '21x' to each side of the equation. 18i2 + 9i2x + -9i2x2 + -21x + 1x2 + 5x3 + 21x + x4 = 18 + 21x Reorder the terms: 18i2 + 9i2x + -9i2x2 + -21x + 21x + 1x2 + 5x3 + x4 = 18 + 21x Combine like terms: -21x + 21x = 0 18i2 + 9i2x + -9i2x2 + 0 + 1x2 + 5x3 + x4 = 18 + 21x 18i2 + 9i2x + -9i2x2 + 1x2 + 5x3 + x4 = 18 + 21x Add '-1x2' to each side of the equation. 18i2 + 9i2x + -9i2x2 + 1x2 + 5x3 + -1x2 + x4 = 18 + 21x + -1x2 Reorder the terms: 18i2 + 9i2x + -9i2x2 + 1x2 + -1x2 + 5x3 + x4 = 18 + 21x + -1x2 Combine like terms: 1x2 + -1x2 = 0 18i2 + 9i2x + -9i2x2 + 0 + 5x3 + x4 = 18 + 21x + -1x2 18i2 + 9i2x + -9i2x2 + 5x3 + x4 = 18 + 21x + -1x2 Add '-5x3' to each side of the equation. 18i2 + 9i2x + -9i2x2 + 5x3 + -5x3 + x4 = 18 + 21x + -1x2 + -5x3 Combine like terms: 5x3 + -5x3 = 0 18i2 + 9i2x + -9i2x2 + 0 + x4 = 18 + 21x + -1x2 + -5x3 18i2 + 9i2x + -9i2x2 + x4 = 18 + 21x + -1x2 + -5x3 Add '-1x4' to each side of the equation. 18i2 + 9i2x + -9i2x2 + x4 + -1x4 = 18 + 21x + -1x2 + -5x3 + -1x4 Combine like terms: x4 + -1x4 = 0 18i2 + 9i2x + -9i2x2 + 0 = 18 + 21x + -1x2 + -5x3 + -1x4 18i2 + 9i2x + -9i2x2 = 18 + 21x + -1x2 + -5x3 + -1x4 Reorder the terms: -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = 18 + 21x + -1x2 + -5x3 + -1x4 + -18 + -21x + x2 + 5x3 + x4 Reorder the terms: -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = 18 + -18 + 21x + -21x + -1x2 + x2 + -5x3 + 5x3 + -1x4 + x4 Combine like terms: 18 + -18 = 0 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = 0 + 21x + -21x + -1x2 + x2 + -5x3 + 5x3 + -1x4 + x4 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = 21x + -21x + -1x2 + x2 + -5x3 + 5x3 + -1x4 + x4 Combine like terms: 21x + -21x = 0 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = 0 + -1x2 + x2 + -5x3 + 5x3 + -1x4 + x4 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = -1x2 + x2 + -5x3 + 5x3 + -1x4 + x4 Combine like terms: -1x2 + x2 = 0 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = 0 + -5x3 + 5x3 + -1x4 + x4 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = -5x3 + 5x3 + -1x4 + x4 Combine like terms: -5x3 + 5x3 = 0 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = 0 + -1x4 + x4 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -18 + 18i2 + 9i2x + -9i2x2 + -21x + x2 + 5x3 + x4 = 0 The solution to this equation could not be determined.
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