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Simplifying (x + -3)[x + -1(6 + -5i)][x + -1(6 + 5i)] = 0 Reorder the terms: (-3 + x)[x + -1(6 + -5i)][x + -1(6 + 5i)] = 0 (-3 + x)[x + (6 * -1 + -5i * -1)][x + -1(6 + 5i)] = 0 (-3 + x)[x + (-6 + 5i)][x + -1(6 + 5i)] = 0 Reorder the terms: (-3 + x)[-6 + 5i + x][x + -1(6 + 5i)] = 0 (-3 + x)[-6 + 5i + x][x + (6 * -1 + 5i * -1)] = 0 (-3 + x)[-6 + 5i + x][x + (-6 + -5i)] = 0 Reorder the terms: (-3 + x)[-6 + 5i + x][-6 + -5i + x] = 0 Multiply (-3 + x) * [-6 + 5i + x] (-3[-6 + 5i + x] + x[-6 + 5i + x])[-6 + -5i + x] = 0 ([-6 * -3 + 5i * -3 + x * -3] + x[-6 + 5i + x])[-6 + -5i + x] = 0 ([18 + -15i + -3x] + x[-6 + 5i + x])[-6 + -5i + x] = 0 (18 + -15i + -3x + [-6 * x + 5i * x + x * x])[-6 + -5i + x] = 0 Reorder the terms: (18 + -15i + -3x + [5ix + -6x + x2])[-6 + -5i + x] = 0 (18 + -15i + -3x + [5ix + -6x + x2])[-6 + -5i + x] = 0 Reorder the terms: (18 + -15i + 5ix + -3x + -6x + x2)[-6 + -5i + x] = 0 Combine like terms: -3x + -6x = -9x (18 + -15i + 5ix + -9x + x2)[-6 + -5i + x] = 0 Multiply (18 + -15i + 5ix + -9x + x2) * [-6 + -5i + x] (18[-6 + -5i + x] + -15i * [-6 + -5i + x] + 5ix * [-6 + -5i + x] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 ([-6 * 18 + -5i * 18 + x * 18] + -15i * [-6 + -5i + x] + 5ix * [-6 + -5i + x] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 ([-108 + -90i + 18x] + -15i * [-6 + -5i + x] + 5ix * [-6 + -5i + x] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 (-108 + -90i + 18x + [-6 * -15i + -5i * -15i + x * -15i] + 5ix * [-6 + -5i + x] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 Reorder the terms: (-108 + -90i + 18x + [90i + -15ix + 75i2] + 5ix * [-6 + -5i + x] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 (-108 + -90i + 18x + [90i + -15ix + 75i2] + 5ix * [-6 + -5i + x] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 (-108 + -90i + 18x + 90i + -15ix + 75i2 + [-6 * 5ix + -5i * 5ix + x * 5ix] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 Reorder the terms: (-108 + -90i + 18x + 90i + -15ix + 75i2 + [-30ix + 5ix2 + -25i2x] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 (-108 + -90i + 18x + 90i + -15ix + 75i2 + [-30ix + 5ix2 + -25i2x] + -9x * [-6 + -5i + x] + x2[-6 + -5i + x]) = 0 (-108 + -90i + 18x + 90i + -15ix + 75i2 + -30ix + 5ix2 + -25i2x + [-6 * -9x + -5i * -9x + x * -9x] + x2[-6 + -5i + x]) = 0 Reorder the terms: (-108 + -90i + 18x + 90i + -15ix + 75i2 + -30ix + 5ix2 + -25i2x + [45ix + 54x + -9x2] + x2[-6 + -5i + x]) = 0 (-108 + -90i + 18x + 90i + -15ix + 75i2 + -30ix + 5ix2 + -25i2x + [45ix + 54x + -9x2] + x2[-6 + -5i + x]) = 0 (-108 + -90i + 18x + 90i + -15ix + 75i2 + -30ix + 5ix2 + -25i2x + 45ix + 54x + -9x2 + [-6 * x2 + -5i * x2 + x * x2]) = 0 Reorder the terms: (-108 + -90i + 18x + 90i + -15ix + 75i2 + -30ix + 5ix2 + -25i2x + 45ix + 54x + -9x2 + [-5ix2 + -6x2 + x3]) = 0 (-108 + -90i + 18x + 90i + -15ix + 75i2 + -30ix + 5ix2 + -25i2x + 45ix + 54x + -9x2 + [-5ix2 + -6x2 + x3]) = 0 Reorder the terms: (-108 + -90i + 90i + -15ix + -30ix + 45ix + 5ix2 + -5ix2 + 75i2 + -25i2x + 18x + 54x + -9x2 + -6x2 + x3) = 0 Combine like terms: -90i + 90i = 0 (-108 + 0 + -15ix + -30ix + 45ix + 5ix2 + -5ix2 + 75i2 + -25i2x + 18x + 54x + -9x2 + -6x2 + x3) = 0 (-108 + -15ix + -30ix + 45ix + 5ix2 + -5ix2 + 75i2 + -25i2x + 18x + 54x + -9x2 + -6x2 + x3) = 0 Combine like terms: -15ix + -30ix = -45ix (-108 + -45ix + 45ix + 5ix2 + -5ix2 + 75i2 + -25i2x + 18x + 54x + -9x2 + -6x2 + x3) = 0 Combine like terms: -45ix + 45ix = 0 (-108 + 0 + 5ix2 + -5ix2 + 75i2 + -25i2x + 18x + 54x + -9x2 + -6x2 + x3) = 0 (-108 + 5ix2 + -5ix2 + 75i2 + -25i2x + 18x + 54x + -9x2 + -6x2 + x3) = 0 Combine like terms: 5ix2 + -5ix2 = 0 (-108 + 0 + 75i2 + -25i2x + 18x + 54x + -9x2 + -6x2 + x3) = 0 (-108 + 75i2 + -25i2x + 18x + 54x + -9x2 + -6x2 + x3) = 0 Combine like terms: 18x + 54x = 72x (-108 + 75i2 + -25i2x + 72x + -9x2 + -6x2 + x3) = 0 Combine like terms: -9x2 + -6x2 = -15x2 (-108 + 75i2 + -25i2x + 72x + -15x2 + x3) = 0 Solving -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '108' to each side of the equation. -108 + 75i2 + -25i2x + 72x + -15x2 + 108 + x3 = 0 + 108 Reorder the terms: -108 + 108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 75i2 + -25i2x + 72x + -15x2 + x3 = 0 + 108 75i2 + -25i2x + 72x + -15x2 + x3 = 0 + 108 Combine like terms: 0 + 108 = 108 75i2 + -25i2x + 72x + -15x2 + x3 = 108 Add '-72x' to each side of the equation. 75i2 + -25i2x + 72x + -15x2 + -72x + x3 = 108 + -72x Reorder the terms: 75i2 + -25i2x + 72x + -72x + -15x2 + x3 = 108 + -72x Combine like terms: 72x + -72x = 0 75i2 + -25i2x + 0 + -15x2 + x3 = 108 + -72x 75i2 + -25i2x + -15x2 + x3 = 108 + -72x Add '15x2' to each side of the equation. 75i2 + -25i2x + -15x2 + 15x2 + x3 = 108 + -72x + 15x2 Combine like terms: -15x2 + 15x2 = 0 75i2 + -25i2x + 0 + x3 = 108 + -72x + 15x2 75i2 + -25i2x + x3 = 108 + -72x + 15x2 Add '-1x3' to each side of the equation. 75i2 + -25i2x + x3 + -1x3 = 108 + -72x + 15x2 + -1x3 Combine like terms: x3 + -1x3 = 0 75i2 + -25i2x + 0 = 108 + -72x + 15x2 + -1x3 75i2 + -25i2x = 108 + -72x + 15x2 + -1x3 Reorder the terms: -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 108 + -72x + 15x2 + -1x3 + -108 + 72x + -15x2 + x3 Reorder the terms: -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 108 + -108 + -72x + 72x + 15x2 + -15x2 + -1x3 + x3 Combine like terms: 108 + -108 = 0 -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 0 + -72x + 72x + 15x2 + -15x2 + -1x3 + x3 -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = -72x + 72x + 15x2 + -15x2 + -1x3 + x3 Combine like terms: -72x + 72x = 0 -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 0 + 15x2 + -15x2 + -1x3 + x3 -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 15x2 + -15x2 + -1x3 + x3 Combine like terms: 15x2 + -15x2 = 0 -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 0 + -1x3 + x3 -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -108 + 75i2 + -25i2x + 72x + -15x2 + x3 = 0 The solution to this equation could not be determined.
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