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Simplifying [x + -1(2 + i)][x + -1(2 + -1i)](x + -3) = 0 [x + (2 * -1 + i * -1)][x + -1(2 + -1i)](x + -3) = 0 [x + (-2 + -1i)][x + -1(2 + -1i)](x + -3) = 0 Reorder the terms: [-2 + -1i + x][x + -1(2 + -1i)](x + -3) = 0 [-2 + -1i + x][x + (2 * -1 + -1i * -1)](x + -3) = 0 [-2 + -1i + x][x + (-2 + 1i)](x + -3) = 0 Reorder the terms: [-2 + -1i + x][-2 + 1i + x](x + -3) = 0 Reorder the terms: [-2 + -1i + x][-2 + 1i + x](-3 + x) = 0 Multiply [-2 + -1i + x] * [-2 + 1i + x] [-2[-2 + 1i + x] + -1i * [-2 + 1i + x] + x[-2 + 1i + x]](-3 + x) = 0 [[-2 * -2 + 1i * -2 + x * -2] + -1i * [-2 + 1i + x] + x[-2 + 1i + x]](-3 + x) = 0 [[4 + -2i + -2x] + -1i * [-2 + 1i + x] + x[-2 + 1i + x]](-3 + x) = 0 [4 + -2i + -2x + [-2 * -1i + 1i * -1i + x * -1i] + x[-2 + 1i + x]](-3 + x) = 0 Reorder the terms: [4 + -2i + -2x + [2i + -1ix + -1i2] + x[-2 + 1i + x]](-3 + x) = 0 [4 + -2i + -2x + [2i + -1ix + -1i2] + x[-2 + 1i + x]](-3 + x) = 0 [4 + -2i + -2x + 2i + -1ix + -1i2 + [-2 * x + 1i * x + x * x]](-3 + x) = 0 Reorder the terms: [4 + -2i + -2x + 2i + -1ix + -1i2 + [1ix + -2x + x2]](-3 + x) = 0 [4 + -2i + -2x + 2i + -1ix + -1i2 + [1ix + -2x + x2]](-3 + x) = 0 Reorder the terms: [4 + -2i + 2i + -1ix + 1ix + -1i2 + -2x + -2x + x2](-3 + x) = 0 Combine like terms: -2i + 2i = 0 [4 + 0 + -1ix + 1ix + -1i2 + -2x + -2x + x2](-3 + x) = 0 [4 + -1ix + 1ix + -1i2 + -2x + -2x + x2](-3 + x) = 0 Combine like terms: -1ix + 1ix = 0 [4 + 0 + -1i2 + -2x + -2x + x2](-3 + x) = 0 [4 + -1i2 + -2x + -2x + x2](-3 + x) = 0 Combine like terms: -2x + -2x = -4x [4 + -1i2 + -4x + x2](-3 + x) = 0 Multiply [4 + -1i2 + -4x + x2] * (-3 + x) [4(-3 + x) + -1i2 * (-3 + x) + -4x * (-3 + x) + x2(-3 + x)] = 0 [(-3 * 4 + x * 4) + -1i2 * (-3 + x) + -4x * (-3 + x) + x2(-3 + x)] = 0 [(-12 + 4x) + -1i2 * (-3 + x) + -4x * (-3 + x) + x2(-3 + x)] = 0 [-12 + 4x + (-3 * -1i2 + x * -1i2) + -4x * (-3 + x) + x2(-3 + x)] = 0 [-12 + 4x + (3i2 + -1i2x) + -4x * (-3 + x) + x2(-3 + x)] = 0 [-12 + 4x + 3i2 + -1i2x + (-3 * -4x + x * -4x) + x2(-3 + x)] = 0 [-12 + 4x + 3i2 + -1i2x + (12x + -4x2) + x2(-3 + x)] = 0 [-12 + 4x + 3i2 + -1i2x + 12x + -4x2 + (-3 * x2 + x * x2)] = 0 [-12 + 4x + 3i2 + -1i2x + 12x + -4x2 + (-3x2 + x3)] = 0 Reorder the terms: [-12 + 3i2 + -1i2x + 4x + 12x + -4x2 + -3x2 + x3] = 0 Combine like terms: 4x + 12x = 16x [-12 + 3i2 + -1i2x + 16x + -4x2 + -3x2 + x3] = 0 Combine like terms: -4x2 + -3x2 = -7x2 [-12 + 3i2 + -1i2x + 16x + -7x2 + x3] = 0 Solving -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 3i2 + -1i2x + 16x + -7x2 + 12 + x3 = 0 + 12 Reorder the terms: -12 + 12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 3i2 + -1i2x + 16x + -7x2 + x3 = 0 + 12 3i2 + -1i2x + 16x + -7x2 + x3 = 0 + 12 Combine like terms: 0 + 12 = 12 3i2 + -1i2x + 16x + -7x2 + x3 = 12 Add '-16x' to each side of the equation. 3i2 + -1i2x + 16x + -7x2 + -16x + x3 = 12 + -16x Reorder the terms: 3i2 + -1i2x + 16x + -16x + -7x2 + x3 = 12 + -16x Combine like terms: 16x + -16x = 0 3i2 + -1i2x + 0 + -7x2 + x3 = 12 + -16x 3i2 + -1i2x + -7x2 + x3 = 12 + -16x Add '7x2' to each side of the equation. 3i2 + -1i2x + -7x2 + 7x2 + x3 = 12 + -16x + 7x2 Combine like terms: -7x2 + 7x2 = 0 3i2 + -1i2x + 0 + x3 = 12 + -16x + 7x2 3i2 + -1i2x + x3 = 12 + -16x + 7x2 Add '-1x3' to each side of the equation. 3i2 + -1i2x + x3 + -1x3 = 12 + -16x + 7x2 + -1x3 Combine like terms: x3 + -1x3 = 0 3i2 + -1i2x + 0 = 12 + -16x + 7x2 + -1x3 3i2 + -1i2x = 12 + -16x + 7x2 + -1x3 Reorder the terms: -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 12 + -16x + 7x2 + -1x3 + -12 + 16x + -7x2 + x3 Reorder the terms: -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 12 + -12 + -16x + 16x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: 12 + -12 = 0 -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 0 + -16x + 16x + 7x2 + -7x2 + -1x3 + x3 -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = -16x + 16x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: -16x + 16x = 0 -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 0 + 7x2 + -7x2 + -1x3 + x3 -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 7x2 + -7x2 + -1x3 + x3 Combine like terms: 7x2 + -7x2 = 0 -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 0 + -1x3 + x3 -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -12 + 3i2 + -1i2x + 16x + -7x2 + x3 = 0 The solution to this equation could not be determined.
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