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Simplifying (3x + 1)(x + 1)(x + 2i)(x + -2i) = 0 Reorder the terms: (1 + 3x)(x + 1)(x + 2i)(x + -2i) = 0 Reorder the terms: (1 + 3x)(1 + x)(x + 2i)(x + -2i) = 0 Reorder the terms: (1 + 3x)(1 + x)(2i + x)(x + -2i) = 0 Reorder the terms: (1 + 3x)(1 + x)(2i + x)(-2i + x) = 0 Multiply (1 + 3x) * (1 + x) (1(1 + x) + 3x * (1 + x))(2i + x)(-2i + x) = 0 ((1 * 1 + x * 1) + 3x * (1 + x))(2i + x)(-2i + x) = 0 ((1 + 1x) + 3x * (1 + x))(2i + x)(-2i + x) = 0 (1 + 1x + (1 * 3x + x * 3x))(2i + x)(-2i + x) = 0 (1 + 1x + (3x + 3x2))(2i + x)(-2i + x) = 0 Combine like terms: 1x + 3x = 4x (1 + 4x + 3x2)(2i + x)(-2i + x) = 0 Multiply (1 + 4x + 3x2) * (2i + x) (1(2i + x) + 4x * (2i + x) + 3x2 * (2i + x))(-2i + x) = 0 ((2i * 1 + x * 1) + 4x * (2i + x) + 3x2 * (2i + x))(-2i + x) = 0 ((2i + 1x) + 4x * (2i + x) + 3x2 * (2i + x))(-2i + x) = 0 (2i + 1x + (2i * 4x + x * 4x) + 3x2 * (2i + x))(-2i + x) = 0 (2i + 1x + (8ix + 4x2) + 3x2 * (2i + x))(-2i + x) = 0 (2i + 1x + 8ix + 4x2 + (2i * 3x2 + x * 3x2))(-2i + x) = 0 (2i + 1x + 8ix + 4x2 + (6ix2 + 3x3))(-2i + x) = 0 Reorder the terms: (2i + 8ix + 6ix2 + 1x + 4x2 + 3x3)(-2i + x) = 0 (2i + 8ix + 6ix2 + 1x + 4x2 + 3x3)(-2i + x) = 0 Multiply (2i + 8ix + 6ix2 + 1x + 4x2 + 3x3) * (-2i + x) (2i * (-2i + x) + 8ix * (-2i + x) + 6ix2 * (-2i + x) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 ((-2i * 2i + x * 2i) + 8ix * (-2i + x) + 6ix2 * (-2i + x) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 Reorder the terms: ((2ix + -4i2) + 8ix * (-2i + x) + 6ix2 * (-2i + x) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 ((2ix + -4i2) + 8ix * (-2i + x) + 6ix2 * (-2i + x) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + (-2i * 8ix + x * 8ix) + 6ix2 * (-2i + x) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 Reorder the terms: (2ix + -4i2 + (8ix2 + -16i2x) + 6ix2 * (-2i + x) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + (8ix2 + -16i2x) + 6ix2 * (-2i + x) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + 8ix2 + -16i2x + (-2i * 6ix2 + x * 6ix2) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 Reorder the terms: (2ix + -4i2 + 8ix2 + -16i2x + (6ix3 + -12i2x2) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + 8ix2 + -16i2x + (6ix3 + -12i2x2) + 1x * (-2i + x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + 8ix2 + -16i2x + 6ix3 + -12i2x2 + (-2i * 1x + x * 1x) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + 8ix2 + -16i2x + 6ix3 + -12i2x2 + (-2ix + 1x2) + 4x2 * (-2i + x) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + 8ix2 + -16i2x + 6ix3 + -12i2x2 + -2ix + 1x2 + (-2i * 4x2 + x * 4x2) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + 8ix2 + -16i2x + 6ix3 + -12i2x2 + -2ix + 1x2 + (-8ix2 + 4x3) + 3x3 * (-2i + x)) = 0 (2ix + -4i2 + 8ix2 + -16i2x + 6ix3 + -12i2x2 + -2ix + 1x2 + -8ix2 + 4x3 + (-2i * 3x3 + x * 3x3)) = 0 (2ix + -4i2 + 8ix2 + -16i2x + 6ix3 + -12i2x2 + -2ix + 1x2 + -8ix2 + 4x3 + (-6ix3 + 3x4)) = 0 Reorder the terms: (2ix + -2ix + 8ix2 + -8ix2 + 6ix3 + -6ix3 + -4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + 3x4) = 0 Combine like terms: 2ix + -2ix = 0 (0 + 8ix2 + -8ix2 + 6ix3 + -6ix3 + -4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + 3x4) = 0 (8ix2 + -8ix2 + 6ix3 + -6ix3 + -4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + 3x4) = 0 Combine like terms: 8ix2 + -8ix2 = 0 (0 + 6ix3 + -6ix3 + -4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + 3x4) = 0 (6ix3 + -6ix3 + -4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + 3x4) = 0 Combine like terms: 6ix3 + -6ix3 = 0 (0 + -4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + 3x4) = 0 (-4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + 3x4) = 0 Solving -4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + 3x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1x2' to each side of the equation. -4i2 + -16i2x + -12i2x2 + 1x2 + 4x3 + -1x2 + 3x4 = 0 + -1x2 Reorder the terms: -4i2 + -16i2x + -12i2x2 + 1x2 + -1x2 + 4x3 + 3x4 = 0 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -4i2 + -16i2x + -12i2x2 + 0 + 4x3 + 3x4 = 0 + -1x2 -4i2 + -16i2x + -12i2x2 + 4x3 + 3x4 = 0 + -1x2 Remove the zero: -4i2 + -16i2x + -12i2x2 + 4x3 + 3x4 = -1x2 Add '-4x3' to each side of the equation. -4i2 + -16i2x + -12i2x2 + 4x3 + -4x3 + 3x4 = -1x2 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -4i2 + -16i2x + -12i2x2 + 0 + 3x4 = -1x2 + -4x3 -4i2 + -16i2x + -12i2x2 + 3x4 = -1x2 + -4x3 Add '-3x4' to each side of the equation. -4i2 + -16i2x + -12i2x2 + 3x4 + -3x4 = -1x2 + -4x3 + -3x4 Combine like terms: 3x4 + -3x4 = 0 -4i2 + -16i2x + -12i2x2 + 0 = -1x2 + -4x3 + -3x4 -4i2 + -16i2x + -12i2x2 = -1x2 + -4x3 + -3x4 Reorder the terms: -4i2 + -16i2x + -12i2x2 + x2 + 4x3 + 3x4 = -1x2 + x2 + -4x3 + 4x3 + -3x4 + 3x4 Combine like terms: -1x2 + x2 = 0 -4i2 + -16i2x + -12i2x2 + x2 + 4x3 + 3x4 = 0 + -4x3 + 4x3 + -3x4 + 3x4 -4i2 + -16i2x + -12i2x2 + x2 + 4x3 + 3x4 = -4x3 + 4x3 + -3x4 + 3x4 Combine like terms: -4x3 + 4x3 = 0 -4i2 + -16i2x + -12i2x2 + x2 + 4x3 + 3x4 = 0 + -3x4 + 3x4 -4i2 + -16i2x + -12i2x2 + x2 + 4x3 + 3x4 = -3x4 + 3x4 Combine like terms: -3x4 + 3x4 = 0 -4i2 + -16i2x + -12i2x2 + x2 + 4x3 + 3x4 = 0 The solution to this equation could not be determined.
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