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Simplifying (x + -3)(x + -1)(-1x + 3i)(-1x + -3i) = 0 Reorder the terms: (-3 + x)(x + -1)(-1x + 3i)(-1x + -3i) = 0 Reorder the terms: (-3 + x)(-1 + x)(-1x + 3i)(-1x + -3i) = 0 Reorder the terms: (-3 + x)(-1 + x)(3i + -1x)(-1x + -3i) = 0 Reorder the terms: (-3 + x)(-1 + x)(3i + -1x)(-3i + -1x) = 0 Multiply (-3 + x) * (-1 + x) (-3(-1 + x) + x(-1 + x))(3i + -1x)(-3i + -1x) = 0 ((-1 * -3 + x * -3) + x(-1 + x))(3i + -1x)(-3i + -1x) = 0 ((3 + -3x) + x(-1 + x))(3i + -1x)(-3i + -1x) = 0 (3 + -3x + (-1 * x + x * x))(3i + -1x)(-3i + -1x) = 0 (3 + -3x + (-1x + x2))(3i + -1x)(-3i + -1x) = 0 Combine like terms: -3x + -1x = -4x (3 + -4x + x2)(3i + -1x)(-3i + -1x) = 0 Multiply (3 + -4x + x2) * (3i + -1x) (3(3i + -1x) + -4x * (3i + -1x) + x2(3i + -1x))(-3i + -1x) = 0 ((3i * 3 + -1x * 3) + -4x * (3i + -1x) + x2(3i + -1x))(-3i + -1x) = 0 ((9i + -3x) + -4x * (3i + -1x) + x2(3i + -1x))(-3i + -1x) = 0 (9i + -3x + (3i * -4x + -1x * -4x) + x2(3i + -1x))(-3i + -1x) = 0 (9i + -3x + (-12ix + 4x2) + x2(3i + -1x))(-3i + -1x) = 0 (9i + -3x + -12ix + 4x2 + (3i * x2 + -1x * x2))(-3i + -1x) = 0 (9i + -3x + -12ix + 4x2 + (3ix2 + -1x3))(-3i + -1x) = 0 Reorder the terms: (9i + -12ix + 3ix2 + -3x + 4x2 + -1x3)(-3i + -1x) = 0 (9i + -12ix + 3ix2 + -3x + 4x2 + -1x3)(-3i + -1x) = 0 Multiply (9i + -12ix + 3ix2 + -3x + 4x2 + -1x3) * (-3i + -1x) (9i * (-3i + -1x) + -12ix * (-3i + -1x) + 3ix2 * (-3i + -1x) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 ((-3i * 9i + -1x * 9i) + -12ix * (-3i + -1x) + 3ix2 * (-3i + -1x) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 Reorder the terms: ((-9ix + -27i2) + -12ix * (-3i + -1x) + 3ix2 * (-3i + -1x) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 ((-9ix + -27i2) + -12ix * (-3i + -1x) + 3ix2 * (-3i + -1x) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + (-3i * -12ix + -1x * -12ix) + 3ix2 * (-3i + -1x) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 Reorder the terms: (-9ix + -27i2 + (12ix2 + 36i2x) + 3ix2 * (-3i + -1x) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + (12ix2 + 36i2x) + 3ix2 * (-3i + -1x) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + 12ix2 + 36i2x + (-3i * 3ix2 + -1x * 3ix2) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 Reorder the terms: (-9ix + -27i2 + 12ix2 + 36i2x + (-3ix3 + -9i2x2) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + 12ix2 + 36i2x + (-3ix3 + -9i2x2) + -3x * (-3i + -1x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + (-3i * -3x + -1x * -3x) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + (9ix + 3x2) + 4x2 * (-3i + -1x) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + 9ix + 3x2 + (-3i * 4x2 + -1x * 4x2) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + 9ix + 3x2 + (-12ix2 + -4x3) + -1x3 * (-3i + -1x)) = 0 (-9ix + -27i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + 9ix + 3x2 + -12ix2 + -4x3 + (-3i * -1x3 + -1x * -1x3)) = 0 (-9ix + -27i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + 9ix + 3x2 + -12ix2 + -4x3 + (3ix3 + 1x4)) = 0 Reorder the terms: (-9ix + 9ix + 12ix2 + -12ix2 + -3ix3 + 3ix3 + -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + 1x4) = 0 Combine like terms: -9ix + 9ix = 0 (0 + 12ix2 + -12ix2 + -3ix3 + 3ix3 + -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + 1x4) = 0 (12ix2 + -12ix2 + -3ix3 + 3ix3 + -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + 1x4) = 0 Combine like terms: 12ix2 + -12ix2 = 0 (0 + -3ix3 + 3ix3 + -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + 1x4) = 0 (-3ix3 + 3ix3 + -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + 1x4) = 0 Combine like terms: -3ix3 + 3ix3 = 0 (0 + -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + 1x4) = 0 (-27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + 1x4) = 0 Solving -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + 1x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3x2' to each side of the equation. -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + -3x2 + 1x4 = 0 + -3x2 Reorder the terms: -27i2 + 36i2x + -9i2x2 + 3x2 + -3x2 + -4x3 + 1x4 = 0 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -27i2 + 36i2x + -9i2x2 + 0 + -4x3 + 1x4 = 0 + -3x2 -27i2 + 36i2x + -9i2x2 + -4x3 + 1x4 = 0 + -3x2 Remove the zero: -27i2 + 36i2x + -9i2x2 + -4x3 + 1x4 = -3x2 Add '4x3' to each side of the equation. -27i2 + 36i2x + -9i2x2 + -4x3 + 4x3 + 1x4 = -3x2 + 4x3 Combine like terms: -4x3 + 4x3 = 0 -27i2 + 36i2x + -9i2x2 + 0 + 1x4 = -3x2 + 4x3 -27i2 + 36i2x + -9i2x2 + 1x4 = -3x2 + 4x3 Add '-1x4' to each side of the equation. -27i2 + 36i2x + -9i2x2 + 1x4 + -1x4 = -3x2 + 4x3 + -1x4 Combine like terms: 1x4 + -1x4 = 0 -27i2 + 36i2x + -9i2x2 + 0 = -3x2 + 4x3 + -1x4 -27i2 + 36i2x + -9i2x2 = -3x2 + 4x3 + -1x4 Reorder the terms: -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + x4 = -3x2 + 3x2 + 4x3 + -4x3 + -1x4 + x4 Combine like terms: -3x2 + 3x2 = 0 -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + x4 = 0 + 4x3 + -4x3 + -1x4 + x4 -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + x4 = 4x3 + -4x3 + -1x4 + x4 Combine like terms: 4x3 + -4x3 = 0 -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + x4 = 0 + -1x4 + x4 -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -27i2 + 36i2x + -9i2x2 + 3x2 + -4x3 + x4 = 0 The solution to this equation could not be determined.
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