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Simplifying (x + -3)(x + -1i)(x + -2)(x + i) = 0 Reorder the terms: (-3 + x)(x + -1i)(x + -2)(x + i) = 0 Reorder the terms: (-3 + x)(-1i + x)(x + -2)(x + i) = 0 Reorder the terms: (-3 + x)(-1i + x)(-2 + x)(x + i) = 0 Reorder the terms: (-3 + x)(-1i + x)(-2 + x)(i + x) = 0 Multiply (-3 + x) * (-1i + x) (-3(-1i + x) + x(-1i + x))(-2 + x)(i + x) = 0 ((-1i * -3 + x * -3) + x(-1i + x))(-2 + x)(i + x) = 0 ((3i + -3x) + x(-1i + x))(-2 + x)(i + x) = 0 (3i + -3x + (-1i * x + x * x))(-2 + x)(i + x) = 0 (3i + -3x + (-1ix + x2))(-2 + x)(i + x) = 0 Reorder the terms: (3i + -1ix + -3x + x2)(-2 + x)(i + x) = 0 (3i + -1ix + -3x + x2)(-2 + x)(i + x) = 0 Multiply (3i + -1ix + -3x + x2) * (-2 + x) (3i * (-2 + x) + -1ix * (-2 + x) + -3x * (-2 + x) + x2(-2 + x))(i + x) = 0 ((-2 * 3i + x * 3i) + -1ix * (-2 + x) + -3x * (-2 + x) + x2(-2 + x))(i + x) = 0 ((-6i + 3ix) + -1ix * (-2 + x) + -3x * (-2 + x) + x2(-2 + x))(i + x) = 0 (-6i + 3ix + (-2 * -1ix + x * -1ix) + -3x * (-2 + x) + x2(-2 + x))(i + x) = 0 (-6i + 3ix + (2ix + -1ix2) + -3x * (-2 + x) + x2(-2 + x))(i + x) = 0 (-6i + 3ix + 2ix + -1ix2 + (-2 * -3x + x * -3x) + x2(-2 + x))(i + x) = 0 (-6i + 3ix + 2ix + -1ix2 + (6x + -3x2) + x2(-2 + x))(i + x) = 0 (-6i + 3ix + 2ix + -1ix2 + 6x + -3x2 + (-2 * x2 + x * x2))(i + x) = 0 (-6i + 3ix + 2ix + -1ix2 + 6x + -3x2 + (-2x2 + x3))(i + x) = 0 Combine like terms: 3ix + 2ix = 5ix (-6i + 5ix + -1ix2 + 6x + -3x2 + -2x2 + x3)(i + x) = 0 Combine like terms: -3x2 + -2x2 = -5x2 (-6i + 5ix + -1ix2 + 6x + -5x2 + x3)(i + x) = 0 Multiply (-6i + 5ix + -1ix2 + 6x + -5x2 + x3) * (i + x) (-6i * (i + x) + 5ix * (i + x) + -1ix2 * (i + x) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 ((i * -6i + x * -6i) + 5ix * (i + x) + -1ix2 * (i + x) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 Reorder the terms: ((-6ix + -6i2) + 5ix * (i + x) + -1ix2 * (i + x) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 ((-6ix + -6i2) + 5ix * (i + x) + -1ix2 * (i + x) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 (-6ix + -6i2 + (i * 5ix + x * 5ix) + -1ix2 * (i + x) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 Reorder the terms: (-6ix + -6i2 + (5ix2 + 5i2x) + -1ix2 * (i + x) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 (-6ix + -6i2 + (5ix2 + 5i2x) + -1ix2 * (i + x) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 (-6ix + -6i2 + 5ix2 + 5i2x + (i * -1ix2 + x * -1ix2) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 Reorder the terms: (-6ix + -6i2 + 5ix2 + 5i2x + (-1ix3 + -1i2x2) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 (-6ix + -6i2 + 5ix2 + 5i2x + (-1ix3 + -1i2x2) + 6x * (i + x) + -5x2 * (i + x) + x3(i + x)) = 0 (-6ix + -6i2 + 5ix2 + 5i2x + -1ix3 + -1i2x2 + (i * 6x + x * 6x) + -5x2 * (i + x) + x3(i + x)) = 0 (-6ix + -6i2 + 5ix2 + 5i2x + -1ix3 + -1i2x2 + (6ix + 6x2) + -5x2 * (i + x) + x3(i + x)) = 0 (-6ix + -6i2 + 5ix2 + 5i2x + -1ix3 + -1i2x2 + 6ix + 6x2 + (i * -5x2 + x * -5x2) + x3(i + x)) = 0 (-6ix + -6i2 + 5ix2 + 5i2x + -1ix3 + -1i2x2 + 6ix + 6x2 + (-5ix2 + -5x3) + x3(i + x)) = 0 (-6ix + -6i2 + 5ix2 + 5i2x + -1ix3 + -1i2x2 + 6ix + 6x2 + -5ix2 + -5x3 + (i * x3 + x * x3)) = 0 (-6ix + -6i2 + 5ix2 + 5i2x + -1ix3 + -1i2x2 + 6ix + 6x2 + -5ix2 + -5x3 + (ix3 + x4)) = 0 Reorder the terms: (-6ix + 6ix + 5ix2 + -5ix2 + -1ix3 + ix3 + -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4) = 0 Combine like terms: -6ix + 6ix = 0 (0 + 5ix2 + -5ix2 + -1ix3 + ix3 + -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4) = 0 (5ix2 + -5ix2 + -1ix3 + ix3 + -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4) = 0 Combine like terms: 5ix2 + -5ix2 = 0 (0 + -1ix3 + ix3 + -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4) = 0 (-1ix3 + ix3 + -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4) = 0 Combine like terms: -1ix3 + ix3 = 0 (0 + -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4) = 0 (-6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4) = 0 Solving -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-6x2' to each side of the equation. -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + -6x2 + x4 = 0 + -6x2 Reorder the terms: -6i2 + 5i2x + -1i2x2 + 6x2 + -6x2 + -5x3 + x4 = 0 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -6i2 + 5i2x + -1i2x2 + 0 + -5x3 + x4 = 0 + -6x2 -6i2 + 5i2x + -1i2x2 + -5x3 + x4 = 0 + -6x2 Remove the zero: -6i2 + 5i2x + -1i2x2 + -5x3 + x4 = -6x2 Add '5x3' to each side of the equation. -6i2 + 5i2x + -1i2x2 + -5x3 + 5x3 + x4 = -6x2 + 5x3 Combine like terms: -5x3 + 5x3 = 0 -6i2 + 5i2x + -1i2x2 + 0 + x4 = -6x2 + 5x3 -6i2 + 5i2x + -1i2x2 + x4 = -6x2 + 5x3 Add '-1x4' to each side of the equation. -6i2 + 5i2x + -1i2x2 + x4 + -1x4 = -6x2 + 5x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -6i2 + 5i2x + -1i2x2 + 0 = -6x2 + 5x3 + -1x4 -6i2 + 5i2x + -1i2x2 = -6x2 + 5x3 + -1x4 Reorder the terms: -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4 = -6x2 + 6x2 + 5x3 + -5x3 + -1x4 + x4 Combine like terms: -6x2 + 6x2 = 0 -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4 = 0 + 5x3 + -5x3 + -1x4 + x4 -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4 = 5x3 + -5x3 + -1x4 + x4 Combine like terms: 5x3 + -5x3 = 0 -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4 = 0 + -1x4 + x4 -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -6i2 + 5i2x + -1i2x2 + 6x2 + -5x3 + x4 = 0 The solution to this equation could not be determined.
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