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Simplifying [x + -1(3 + 3i)][x + -1(3 + -3i)](x + 1)(x + -2) = 0 [x + (3 * -1 + 3i * -1)][x + -1(3 + -3i)](x + 1)(x + -2) = 0 [x + (-3 + -3i)][x + -1(3 + -3i)](x + 1)(x + -2) = 0 Reorder the terms: [-3 + -3i + x][x + -1(3 + -3i)](x + 1)(x + -2) = 0 [-3 + -3i + x][x + (3 * -1 + -3i * -1)](x + 1)(x + -2) = 0 [-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 = 3x [9 + -9i2 + -9i2x + 3x + -6x2 + 1x2 + x3](-2 + x) = 0 Combine like terms: -6x2 + 1x2 = -5x2 [9 + -9i2 + -9i2x + 3x + -5x2 + x3](-2 + x) = 0 Multiply [9 + -9i2 + -9i2x + 3x + -5x2 + x3] * (-2 + x) [9(-2 + x) + -9i2 * (-2 + x) + -9i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [(-2 * 9 + x * 9) + -9i2 * (-2 + x) + -9i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [(-18 + 9x) + -9i2 * (-2 + x) + -9i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [-18 + 9x + (-2 * -9i2 + x * -9i2) + -9i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [-18 + 9x + (18i2 + -9i2x) + -9i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [-18 + 9x + 18i2 + -9i2x + (-2 * -9i2x + x * -9i2x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [-18 + 9x + 18i2 + -9i2x + (18i2x + -9i2x2) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + (-2 * 3x + x * 3x) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + (-6x + 3x2) + -5x2 * (-2 + x) + x3(-2 + x)] = 0 [-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + -6x + 3x2 + (-2 * -5x2 + x * -5x2) + x3(-2 + x)] = 0 [-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + -6x + 3x2 + (10x2 + -5x3) + x3(-2 + x)] = 0 [-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + -6x + 3x2 + 10x2 + -5x3 + (-2 * x3 + x * x3)] = 0 [-18 + 9x + 18i2 + -9i2x + 18i2x + -9i2x2 + -6x + 3x2 + 10x2 + -5x3 + (-2x3 + x4)] = 0 Reorder the terms: [-18 + 18i2 + -9i2x + 18i2x + -9i2x2 + 9x + -6x + 3x2 + 10x2 + -5x3 + -2x3 + x4] = 0 Combine like terms: -9i2x + 18i2x = 9i2x [-18 + 18i2 + 9i2x + -9i2x2 + 9x + -6x + 3x2 + 10x2 + -5x3 + -2x3 + x4] = 0 Combine like terms: 9x + -6x = 3x [-18 + 18i2 + 9i2x + -9i2x2 + 3x + 3x2 + 10x2 + -5x3 + -2x3 + x4] = 0 Combine like terms: 3x2 + 10x2 = 13x2 [-18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -5x3 + -2x3 + x4] = 0 Combine like terms: -5x3 + -2x3 = -7x3 [-18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4] = 0 Solving -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + 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 + 3x + 13x2 + -7x3 + 18 + x4 = 0 + 18 Reorder the terms: -18 + 18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 0 + 18 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 0 + 18 Combine like terms: 0 + 18 = 18 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 18 Add '-3x' to each side of the equation. 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + -3x + x4 = 18 + -3x Reorder the terms: 18i2 + 9i2x + -9i2x2 + 3x + -3x + 13x2 + -7x3 + x4 = 18 + -3x Combine like terms: 3x + -3x = 0 18i2 + 9i2x + -9i2x2 + 0 + 13x2 + -7x3 + x4 = 18 + -3x 18i2 + 9i2x + -9i2x2 + 13x2 + -7x3 + x4 = 18 + -3x Add '-13x2' to each side of the equation. 18i2 + 9i2x + -9i2x2 + 13x2 + -7x3 + -13x2 + x4 = 18 + -3x + -13x2 Reorder the terms: 18i2 + 9i2x + -9i2x2 + 13x2 + -13x2 + -7x3 + x4 = 18 + -3x + -13x2 Combine like terms: 13x2 + -13x2 = 0 18i2 + 9i2x + -9i2x2 + 0 + -7x3 + x4 = 18 + -3x + -13x2 18i2 + 9i2x + -9i2x2 + -7x3 + x4 = 18 + -3x + -13x2 Add '7x3' to each side of the equation. 18i2 + 9i2x + -9i2x2 + -7x3 + 7x3 + x4 = 18 + -3x + -13x2 + 7x3 Combine like terms: -7x3 + 7x3 = 0 18i2 + 9i2x + -9i2x2 + 0 + x4 = 18 + -3x + -13x2 + 7x3 18i2 + 9i2x + -9i2x2 + x4 = 18 + -3x + -13x2 + 7x3 Add '-1x4' to each side of the equation. 18i2 + 9i2x + -9i2x2 + x4 + -1x4 = 18 + -3x + -13x2 + 7x3 + -1x4 Combine like terms: x4 + -1x4 = 0 18i2 + 9i2x + -9i2x2 + 0 = 18 + -3x + -13x2 + 7x3 + -1x4 18i2 + 9i2x + -9i2x2 = 18 + -3x + -13x2 + 7x3 + -1x4 Reorder the terms: -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 18 + -3x + -13x2 + 7x3 + -1x4 + -18 + 3x + 13x2 + -7x3 + x4 Reorder the terms: -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 18 + -18 + -3x + 3x + -13x2 + 13x2 + 7x3 + -7x3 + -1x4 + x4 Combine like terms: 18 + -18 = 0 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 0 + -3x + 3x + -13x2 + 13x2 + 7x3 + -7x3 + -1x4 + x4 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = -3x + 3x + -13x2 + 13x2 + 7x3 + -7x3 + -1x4 + x4 Combine like terms: -3x + 3x = 0 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 0 + -13x2 + 13x2 + 7x3 + -7x3 + -1x4 + x4 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = -13x2 + 13x2 + 7x3 + -7x3 + -1x4 + x4 Combine like terms: -13x2 + 13x2 = 0 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 0 + 7x3 + -7x3 + -1x4 + x4 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 7x3 + -7x3 + -1x4 + x4 Combine like terms: 7x3 + -7x3 = 0 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 0 + -1x4 + x4 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -18 + 18i2 + 9i2x + -9i2x2 + 3x + 13x2 + -7x3 + x4 = 0 The solution to this equation could not be determined.
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