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Simplifying (x + -2)(x + 3 + 3i)(x + 3 + -3i) = 0 Reorder the terms: (-2 + x)(x + 3 + 3i)(x + 3 + -3i) = 0 Reorder the terms: (-2 + x)(3 + 3i + x)(x + 3 + -3i) = 0 Reorder the terms: (-2 + x)(3 + 3i + x)(3 + -3i + x) = 0 Multiply (-2 + x) * (3 + 3i + x) (-2(3 + 3i + x) + x(3 + 3i + x))(3 + -3i + x) = 0 ((3 * -2 + 3i * -2 + x * -2) + x(3 + 3i + x))(3 + -3i + x) = 0 ((-6 + -6i + -2x) + x(3 + 3i + x))(3 + -3i + x) = 0 (-6 + -6i + -2x + (3 * x + 3i * x + x * x))(3 + -3i + x) = 0 Reorder the terms: (-6 + -6i + -2x + (3ix + 3x + x2))(3 + -3i + x) = 0 (-6 + -6i + -2x + (3ix + 3x + x2))(3 + -3i + x) = 0 Reorder the terms: (-6 + -6i + 3ix + -2x + 3x + x2)(3 + -3i + x) = 0 Combine like terms: -2x + 3x = 1x (-6 + -6i + 3ix + 1x + x2)(3 + -3i + x) = 0 Multiply (-6 + -6i + 3ix + 1x + x2) * (3 + -3i + x) (-6(3 + -3i + x) + -6i * (3 + -3i + x) + 3ix * (3 + -3i + x) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 ((3 * -6 + -3i * -6 + x * -6) + -6i * (3 + -3i + x) + 3ix * (3 + -3i + x) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 ((-18 + 18i + -6x) + -6i * (3 + -3i + x) + 3ix * (3 + -3i + x) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 (-18 + 18i + -6x + (3 * -6i + -3i * -6i + x * -6i) + 3ix * (3 + -3i + x) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 Reorder the terms: (-18 + 18i + -6x + (-18i + -6ix + 18i2) + 3ix * (3 + -3i + x) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 (-18 + 18i + -6x + (-18i + -6ix + 18i2) + 3ix * (3 + -3i + x) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 (-18 + 18i + -6x + -18i + -6ix + 18i2 + (3 * 3ix + -3i * 3ix + x * 3ix) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 Reorder the terms: (-18 + 18i + -6x + -18i + -6ix + 18i2 + (9ix + 3ix2 + -9i2x) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 (-18 + 18i + -6x + -18i + -6ix + 18i2 + (9ix + 3ix2 + -9i2x) + 1x * (3 + -3i + x) + x2(3 + -3i + x)) = 0 (-18 + 18i + -6x + -18i + -6ix + 18i2 + 9ix + 3ix2 + -9i2x + (3 * 1x + -3i * 1x + x * 1x) + x2(3 + -3i + x)) = 0 Reorder the terms: (-18 + 18i + -6x + -18i + -6ix + 18i2 + 9ix + 3ix2 + -9i2x + (-3ix + 3x + 1x2) + x2(3 + -3i + x)) = 0 (-18 + 18i + -6x + -18i + -6ix + 18i2 + 9ix + 3ix2 + -9i2x + (-3ix + 3x + 1x2) + x2(3 + -3i + x)) = 0 (-18 + 18i + -6x + -18i + -6ix + 18i2 + 9ix + 3ix2 + -9i2x + -3ix + 3x + 1x2 + (3 * x2 + -3i * x2 + x * x2)) = 0 Reorder the terms: (-18 + 18i + -6x + -18i + -6ix + 18i2 + 9ix + 3ix2 + -9i2x + -3ix + 3x + 1x2 + (-3ix2 + 3x2 + x3)) = 0 (-18 + 18i + -6x + -18i + -6ix + 18i2 + 9ix + 3ix2 + -9i2x + -3ix + 3x + 1x2 + (-3ix2 + 3x2 + x3)) = 0 Reorder the terms: (-18 + 18i + -18i + -6ix + 9ix + -3ix + 3ix2 + -3ix2 + 18i2 + -9i2x + -6x + 3x + 1x2 + 3x2 + x3) = 0 Combine like terms: 18i + -18i = 0 (-18 + 0 + -6ix + 9ix + -3ix + 3ix2 + -3ix2 + 18i2 + -9i2x + -6x + 3x + 1x2 + 3x2 + x3) = 0 (-18 + -6ix + 9ix + -3ix + 3ix2 + -3ix2 + 18i2 + -9i2x + -6x + 3x + 1x2 + 3x2 + x3) = 0 Combine like terms: -6ix + 9ix = 3ix (-18 + 3ix + -3ix + 3ix2 + -3ix2 + 18i2 + -9i2x + -6x + 3x + 1x2 + 3x2 + x3) = 0 Combine like terms: 3ix + -3ix = 0 (-18 + 0 + 3ix2 + -3ix2 + 18i2 + -9i2x + -6x + 3x + 1x2 + 3x2 + x3) = 0 (-18 + 3ix2 + -3ix2 + 18i2 + -9i2x + -6x + 3x + 1x2 + 3x2 + x3) = 0 Combine like terms: 3ix2 + -3ix2 = 0 (-18 + 0 + 18i2 + -9i2x + -6x + 3x + 1x2 + 3x2 + x3) = 0 (-18 + 18i2 + -9i2x + -6x + 3x + 1x2 + 3x2 + x3) = 0 Combine like terms: -6x + 3x = -3x (-18 + 18i2 + -9i2x + -3x + 1x2 + 3x2 + x3) = 0 Combine like terms: 1x2 + 3x2 = 4x2 (-18 + 18i2 + -9i2x + -3x + 4x2 + x3) = 0 Solving -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 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 + -3x + 4x2 + 18 + x3 = 0 + 18 Reorder the terms: -18 + 18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 18i2 + -9i2x + -3x + 4x2 + x3 = 0 + 18 18i2 + -9i2x + -3x + 4x2 + x3 = 0 + 18 Combine like terms: 0 + 18 = 18 18i2 + -9i2x + -3x + 4x2 + x3 = 18 Add '3x' to each side of the equation. 18i2 + -9i2x + -3x + 4x2 + 3x + x3 = 18 + 3x Reorder the terms: 18i2 + -9i2x + -3x + 3x + 4x2 + x3 = 18 + 3x Combine like terms: -3x + 3x = 0 18i2 + -9i2x + 0 + 4x2 + x3 = 18 + 3x 18i2 + -9i2x + 4x2 + x3 = 18 + 3x Add '-4x2' to each side of the equation. 18i2 + -9i2x + 4x2 + -4x2 + x3 = 18 + 3x + -4x2 Combine like terms: 4x2 + -4x2 = 0 18i2 + -9i2x + 0 + x3 = 18 + 3x + -4x2 18i2 + -9i2x + x3 = 18 + 3x + -4x2 Add '-1x3' to each side of the equation. 18i2 + -9i2x + x3 + -1x3 = 18 + 3x + -4x2 + -1x3 Combine like terms: x3 + -1x3 = 0 18i2 + -9i2x + 0 = 18 + 3x + -4x2 + -1x3 18i2 + -9i2x = 18 + 3x + -4x2 + -1x3 Reorder the terms: -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 18 + 3x + -4x2 + -1x3 + -18 + -3x + 4x2 + x3 Reorder the terms: -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 18 + -18 + 3x + -3x + -4x2 + 4x2 + -1x3 + x3 Combine like terms: 18 + -18 = 0 -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 0 + 3x + -3x + -4x2 + 4x2 + -1x3 + x3 -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 3x + -3x + -4x2 + 4x2 + -1x3 + x3 Combine like terms: 3x + -3x = 0 -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 0 + -4x2 + 4x2 + -1x3 + x3 -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = -4x2 + 4x2 + -1x3 + x3 Combine like terms: -4x2 + 4x2 = 0 -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 0 + -1x3 + x3 -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -18 + 18i2 + -9i2x + -3x + 4x2 + x3 = 0 The solution to this equation could not be determined.
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