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Simplifying (x + -3)(x + -2 + i)(x + -2 + -1i) = 0 Reorder the terms: (-3 + x)(x + -2 + i)(x + -2 + -1i) = 0 Reorder the terms: (-3 + x)(-2 + i + x)(x + -2 + -1i) = 0 Reorder the terms: (-3 + x)(-2 + i + x)(-2 + -1i + x) = 0 Multiply (-3 + x) * (-2 + i + x) (-3(-2 + i + x) + x(-2 + i + x))(-2 + -1i + x) = 0 ((-2 * -3 + i * -3 + x * -3) + x(-2 + i + x))(-2 + -1i + x) = 0 ((6 + -3i + -3x) + x(-2 + i + x))(-2 + -1i + x) = 0 (6 + -3i + -3x + (-2 * x + i * x + x * x))(-2 + -1i + x) = 0 Reorder the terms: (6 + -3i + -3x + (ix + -2x + x2))(-2 + -1i + x) = 0 (6 + -3i + -3x + (ix + -2x + x2))(-2 + -1i + x) = 0 Reorder the terms: (6 + -3i + ix + -3x + -2x + x2)(-2 + -1i + x) = 0 Combine like terms: -3x + -2x = -5x (6 + -3i + ix + -5x + x2)(-2 + -1i + x) = 0 Multiply (6 + -3i + ix + -5x + x2) * (-2 + -1i + x) (6(-2 + -1i + x) + -3i * (-2 + -1i + x) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 ((-2 * 6 + -1i * 6 + x * 6) + -3i * (-2 + -1i + x) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 ((-12 + -6i + 6x) + -3i * (-2 + -1i + x) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-12 + -6i + 6x + (-2 * -3i + -1i * -3i + x * -3i) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-12 + -6i + 6x + (6i + -3ix + 3i2) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-12 + -6i + 6x + (6i + -3ix + 3i2) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-12 + -6i + 6x + 6i + -3ix + 3i2 + (-2 * ix + -1i * ix + x * ix) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-12 + -6i + 6x + 6i + -3ix + 3i2 + (-2ix + ix2 + -1i2x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-12 + -6i + 6x + 6i + -3ix + 3i2 + (-2ix + ix2 + -1i2x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + (-2 * -5x + -1i * -5x + x * -5x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + (5ix + 10x + -5x2) + x2(-2 + -1i + x)) = 0 (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + (5ix + 10x + -5x2) + x2(-2 + -1i + x)) = 0 (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + 5ix + 10x + -5x2 + (-2 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + 5ix + 10x + -5x2 + (-1ix2 + -2x2 + x3)) = 0 (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + 5ix + 10x + -5x2 + (-1ix2 + -2x2 + x3)) = 0 Reorder the terms: (-12 + -6i + 6i + -3ix + -2ix + 5ix + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3) = 0 Combine like terms: -6i + 6i = 0 (-12 + 0 + -3ix + -2ix + 5ix + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3) = 0 (-12 + -3ix + -2ix + 5ix + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3) = 0 Combine like terms: -3ix + -2ix = -5ix (-12 + -5ix + 5ix + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3) = 0 Combine like terms: -5ix + 5ix = 0 (-12 + 0 + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3) = 0 (-12 + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (-12 + 0 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3) = 0 (-12 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3) = 0 Combine like terms: 6x + 10x = 16x (-12 + 3i2 + -1i2x + 16x + -5x2 + -2x2 + x3) = 0 Combine like terms: -5x2 + -2x2 = -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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