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Simplifying (x + 1)[x + -1(3 + -4i)][x + -1(3 + 4i)] = 0 Reorder the terms: (1 + x)[x + -1(3 + -4i)][x + -1(3 + 4i)] = 0 (1 + x)[x + (3 * -1 + -4i * -1)][x + -1(3 + 4i)] = 0 (1 + x)[x + (-3 + 4i)][x + -1(3 + 4i)] = 0 Reorder the terms: (1 + x)[-3 + 4i + x][x + -1(3 + 4i)] = 0 (1 + x)[-3 + 4i + x][x + (3 * -1 + 4i * -1)] = 0 (1 + x)[-3 + 4i + x][x + (-3 + -4i)] = 0 Reorder the terms: (1 + x)[-3 + 4i + x][-3 + -4i + x] = 0 Multiply (1 + x) * [-3 + 4i + x] (1[-3 + 4i + x] + x[-3 + 4i + x])[-3 + -4i + x] = 0 ([-3 * 1 + 4i * 1 + x * 1] + x[-3 + 4i + x])[-3 + -4i + x] = 0 ([-3 + 4i + 1x] + x[-3 + 4i + x])[-3 + -4i + x] = 0 (-3 + 4i + 1x + [-3 * x + 4i * x + x * x])[-3 + -4i + x] = 0 Reorder the terms: (-3 + 4i + 1x + [4ix + -3x + x2])[-3 + -4i + x] = 0 (-3 + 4i + 1x + [4ix + -3x + x2])[-3 + -4i + x] = 0 Reorder the terms: (-3 + 4i + 4ix + 1x + -3x + x2)[-3 + -4i + x] = 0 Combine like terms: 1x + -3x = -2x (-3 + 4i + 4ix + -2x + x2)[-3 + -4i + x] = 0 Multiply (-3 + 4i + 4ix + -2x + x2) * [-3 + -4i + x] (-3[-3 + -4i + x] + 4i * [-3 + -4i + x] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 ([-3 * -3 + -4i * -3 + x * -3] + 4i * [-3 + -4i + x] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 ([9 + 12i + -3x] + 4i * [-3 + -4i + x] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 (9 + 12i + -3x + [-3 * 4i + -4i * 4i + x * 4i] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 Reorder the terms: (9 + 12i + -3x + [-12i + 4ix + -16i2] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 (9 + 12i + -3x + [-12i + 4ix + -16i2] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 (9 + 12i + -3x + -12i + 4ix + -16i2 + [-3 * 4ix + -4i * 4ix + x * 4ix] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 Reorder the terms: (9 + 12i + -3x + -12i + 4ix + -16i2 + [-12ix + 4ix2 + -16i2x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 (9 + 12i + -3x + -12i + 4ix + -16i2 + [-12ix + 4ix2 + -16i2x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0 (9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + [-3 * -2x + -4i * -2x + x * -2x] + x2[-3 + -4i + x]) = 0 Reorder the terms: (9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + [8ix + 6x + -2x2] + x2[-3 + -4i + x]) = 0 (9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + [8ix + 6x + -2x2] + x2[-3 + -4i + x]) = 0 (9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + 8ix + 6x + -2x2 + [-3 * x2 + -4i * x2 + x * x2]) = 0 Reorder the terms: (9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + 8ix + 6x + -2x2 + [-4ix2 + -3x2 + x3]) = 0 (9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + 8ix + 6x + -2x2 + [-4ix2 + -3x2 + x3]) = 0 Reorder the terms: (9 + 12i + -12i + 4ix + -12ix + 8ix + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0 Combine like terms: 12i + -12i = 0 (9 + 0 + 4ix + -12ix + 8ix + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0 (9 + 4ix + -12ix + 8ix + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0 Combine like terms: 4ix + -12ix = -8ix (9 + -8ix + 8ix + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0 Combine like terms: -8ix + 8ix = 0 (9 + 0 + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0 (9 + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0 Combine like terms: 4ix2 + -4ix2 = 0 (9 + 0 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0 (9 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0 Combine like terms: -3x + 6x = 3x (9 + -16i2 + -16i2x + 3x + -2x2 + -3x2 + x3) = 0 Combine like terms: -2x2 + -3x2 = -5x2 (9 + -16i2 + -16i2x + 3x + -5x2 + x3) = 0 Solving 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -16i2 + -16i2x + 3x + -5x2 + -9 + x3 = 0 + -9 Reorder the terms: 9 + -9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -9 -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -9 Combine like terms: 0 + -9 = -9 -16i2 + -16i2x + 3x + -5x2 + x3 = -9 Add '-3x' to each side of the equation. -16i2 + -16i2x + 3x + -5x2 + -3x + x3 = -9 + -3x Reorder the terms: -16i2 + -16i2x + 3x + -3x + -5x2 + x3 = -9 + -3x Combine like terms: 3x + -3x = 0 -16i2 + -16i2x + 0 + -5x2 + x3 = -9 + -3x -16i2 + -16i2x + -5x2 + x3 = -9 + -3x Add '5x2' to each side of the equation. -16i2 + -16i2x + -5x2 + 5x2 + x3 = -9 + -3x + 5x2 Combine like terms: -5x2 + 5x2 = 0 -16i2 + -16i2x + 0 + x3 = -9 + -3x + 5x2 -16i2 + -16i2x + x3 = -9 + -3x + 5x2 Add '-1x3' to each side of the equation. -16i2 + -16i2x + x3 + -1x3 = -9 + -3x + 5x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -16i2 + -16i2x + 0 = -9 + -3x + 5x2 + -1x3 -16i2 + -16i2x = -9 + -3x + 5x2 + -1x3 Reorder the terms: 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = -9 + -3x + 5x2 + -1x3 + 9 + 3x + -5x2 + x3 Reorder the terms: 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = -9 + 9 + -3x + 3x + 5x2 + -5x2 + -1x3 + x3 Combine like terms: -9 + 9 = 0 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -3x + 3x + 5x2 + -5x2 + -1x3 + x3 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = -3x + 3x + 5x2 + -5x2 + -1x3 + x3 Combine like terms: -3x + 3x = 0 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + 5x2 + -5x2 + -1x3 + x3 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3 Combine like terms: 5x2 + -5x2 = 0 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -1x3 + x3 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 The solution to this equation could not be determined.
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