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Simplifying [x + -1(3 + 3i)][x + -1(3 + -3i)](x + 2)(x + -1) = 0 [x + (3 * -1 + 3i * -1)][x + -1(3 + -3i)](x + 2)(x + -1) = 0 [x + (-3 + -3i)][x + -1(3 + -3i)](x + 2)(x + -1) = 0 Reorder the terms: [-3 + -3i + x][x + -1(3 + -3i)](x + 2)(x + -1) = 0 [-3 + -3i + x][x + (3 * -1 + -3i * -1)](x + 2)(x + -1) = 0 [-3 + -3i + x][x + (-3 + 3i)](x + 2)(x + -1) = 0 Reorder the terms: [-3 + -3i + x][-3 + 3i + x](x + 2)(x + -1) = 0 Reorder the terms: [-3 + -3i + x][-3 + 3i + x](2 + x)(x + -1) = 0 Reorder the terms: [-3 + -3i + x][-3 + 3i + x](2 + x)(-1 + x) = 0 Multiply [-3 + -3i + x] * [-3 + 3i + x] [-3[-3 + 3i + x] + -3i * [-3 + 3i + x] + x[-3 + 3i + x]](2 + x)(-1 + x) = 0 [[-3 * -3 + 3i * -3 + x * -3] + -3i * [-3 + 3i + x] + x[-3 + 3i + x]](2 + x)(-1 + x) = 0 [[9 + -9i + -3x] + -3i * [-3 + 3i + x] + x[-3 + 3i + x]](2 + x)(-1 + x) = 0 [9 + -9i + -3x + [-3 * -3i + 3i * -3i + x * -3i] + x[-3 + 3i + x]](2 + x)(-1 + x) = 0 Reorder the terms: [9 + -9i + -3x + [9i + -3ix + -9i2] + x[-3 + 3i + x]](2 + x)(-1 + x) = 0 [9 + -9i + -3x + [9i + -3ix + -9i2] + x[-3 + 3i + x]](2 + x)(-1 + x) = 0 [9 + -9i + -3x + 9i + -3ix + -9i2 + [-3 * x + 3i * x + x * x]](2 + x)(-1 + x) = 0 Reorder the terms: [9 + -9i + -3x + 9i + -3ix + -9i2 + [3ix + -3x + x2]](2 + x)(-1 + x) = 0 [9 + -9i + -3x + 9i + -3ix + -9i2 + [3ix + -3x + x2]](2 + x)(-1 + x) = 0 Reorder the terms: [9 + -9i + 9i + -3ix + 3ix + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) = 0 Combine like terms: -9i + 9i = 0 [9 + 0 + -3ix + 3ix + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) = 0 [9 + -3ix + 3ix + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) = 0 Combine like terms: -3ix + 3ix = 0 [9 + 0 + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) = 0 [9 + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) = 0 Combine like terms: -3x + -3x = -6x [9 + -9i2 + -6x + x2](2 + x)(-1 + x) = 0 Multiply [9 + -9i2 + -6x + x2] * (2 + x) [9(2 + x) + -9i2 * (2 + x) + -6x * (2 + x) + x2(2 + x)](-1 + x) = 0 [(2 * 9 + x * 9) + -9i2 * (2 + x) + -6x * (2 + x) + x2(2 + x)](-1 + x) = 0 [(18 + 9x) + -9i2 * (2 + x) + -6x * (2 + x) + x2(2 + x)](-1 + x) = 0 [18 + 9x + (2 * -9i2 + x * -9i2) + -6x * (2 + x) + x2(2 + x)](-1 + x) = 0 [18 + 9x + (-18i2 + -9i2x) + -6x * (2 + x) + x2(2 + x)](-1 + x) = 0 [18 + 9x + -18i2 + -9i2x + (2 * -6x + x * -6x) + x2(2 + x)](-1 + x) = 0 [18 + 9x + -18i2 + -9i2x + (-12x + -6x2) + x2(2 + x)](-1 + x) = 0 [18 + 9x + -18i2 + -9i2x + -12x + -6x2 + (2 * x2 + x * x2)](-1 + x) = 0 [18 + 9x + -18i2 + -9i2x + -12x + -6x2 + (2x2 + x3)](-1 + x) = 0 Reorder the terms: [18 + -18i2 + -9i2x + 9x + -12x + -6x2 + 2x2 + x3](-1 + x) = 0 Combine like terms: 9x + -12x = -3x [18 + -18i2 + -9i2x + -3x + -6x2 + 2x2 + x3](-1 + x) = 0 Combine like terms: -6x2 + 2x2 = -4x2 [18 + -18i2 + -9i2x + -3x + -4x2 + x3](-1 + x) = 0 Multiply [18 + -18i2 + -9i2x + -3x + -4x2 + x3] * (-1 + x) [18(-1 + x) + -18i2 * (-1 + x) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [(-1 * 18 + x * 18) + -18i2 * (-1 + x) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [(-18 + 18x) + -18i2 * (-1 + x) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [-18 + 18x + (-1 * -18i2 + x * -18i2) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [-18 + 18x + (18i2 + -18i2x) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [-18 + 18x + 18i2 + -18i2x + (-1 * -9i2x + x * -9i2x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [-18 + 18x + 18i2 + -18i2x + (9i2x + -9i2x2) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + (-1 * -3x + x * -3x) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + (3x + -3x2) + -4x2 * (-1 + x) + x3(-1 + x)] = 0 [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + 3x + -3x2 + (-1 * -4x2 + x * -4x2) + x3(-1 + x)] = 0 [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + 3x + -3x2 + (4x2 + -4x3) + x3(-1 + x)] = 0 [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + 3x + -3x2 + 4x2 + -4x3 + (-1 * x3 + x * x3)] = 0 [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + 3x + -3x2 + 4x2 + -4x3 + (-1x3 + x4)] = 0 Reorder the terms: [-18 + 18i2 + -18i2x + 9i2x + -9i2x2 + 18x + 3x + -3x2 + 4x2 + -4x3 + -1x3 + x4] = 0 Combine like terms: -18i2x + 9i2x = -9i2x [-18 + 18i2 + -9i2x + -9i2x2 + 18x + 3x + -3x2 + 4x2 + -4x3 + -1x3 + x4] = 0 Combine like terms: 18x + 3x = 21x [-18 + 18i2 + -9i2x + -9i2x2 + 21x + -3x2 + 4x2 + -4x3 + -1x3 + x4] = 0 Combine like terms: -3x2 + 4x2 = 1x2 [-18 + 18i2 + -9i2x + -9i2x2 + 21x + 1x2 + -4x3 + -1x3 + x4] = 0 Combine like terms: -4x3 + -1x3 = -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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