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Simplifying (x + -4)(x + 8)(x + -1(2x + 3i))(x + -1(2x + -3i)) = 0 Reorder the terms: (-4 + x)(x + 8)(x + -1(2x + 3i))(x + -1(2x + -3i)) = 0 Reorder the terms: (-4 + x)(8 + x)(x + -1(2x + 3i))(x + -1(2x + -3i)) = 0 Reorder the terms: (-4 + x)(8 + x)(x + -1(3i + 2x))(x + -1(2x + -3i)) = 0 (-4 + x)(8 + x)(x + (3i * -1 + 2x * -1))(x + -1(2x + -3i)) = 0 (-4 + x)(8 + x)(x + (-3i + -2x))(x + -1(2x + -3i)) = 0 Reorder the terms: (-4 + x)(8 + x)(-3i + x + -2x)(x + -1(2x + -3i)) = 0 Combine like terms: x + -2x = -1x (-4 + x)(8 + x)(-3i + -1x)(x + -1(2x + -3i)) = 0 Reorder the terms: (-4 + x)(8 + x)(-3i + -1x)(x + -1(-3i + 2x)) = 0 (-4 + x)(8 + x)(-3i + -1x)(x + (-3i * -1 + 2x * -1)) = 0 (-4 + x)(8 + x)(-3i + -1x)(x + (3i + -2x)) = 0 Reorder the terms: (-4 + x)(8 + x)(-3i + -1x)(3i + x + -2x) = 0 Combine like terms: x + -2x = -1x (-4 + x)(8 + x)(-3i + -1x)(3i + -1x) = 0 Multiply (-4 + x) * (8 + x) (-4(8 + x) + x(8 + x))(-3i + -1x)(3i + -1x) = 0 ((8 * -4 + x * -4) + x(8 + x))(-3i + -1x)(3i + -1x) = 0 ((-32 + -4x) + x(8 + x))(-3i + -1x)(3i + -1x) = 0 (-32 + -4x + (8 * x + x * x))(-3i + -1x)(3i + -1x) = 0 (-32 + -4x + (8x + x2))(-3i + -1x)(3i + -1x) = 0 Combine like terms: -4x + 8x = 4x (-32 + 4x + x2)(-3i + -1x)(3i + -1x) = 0 Multiply (-32 + 4x + x2) * (-3i + -1x) (-32(-3i + -1x) + 4x * (-3i + -1x) + x2(-3i + -1x))(3i + -1x) = 0 ((-3i * -32 + -1x * -32) + 4x * (-3i + -1x) + x2(-3i + -1x))(3i + -1x) = 0 ((96i + 32x) + 4x * (-3i + -1x) + x2(-3i + -1x))(3i + -1x) = 0 (96i + 32x + (-3i * 4x + -1x * 4x) + x2(-3i + -1x))(3i + -1x) = 0 (96i + 32x + (-12ix + -4x2) + x2(-3i + -1x))(3i + -1x) = 0 (96i + 32x + -12ix + -4x2 + (-3i * x2 + -1x * x2))(3i + -1x) = 0 (96i + 32x + -12ix + -4x2 + (-3ix2 + -1x3))(3i + -1x) = 0 Reorder the terms: (96i + -12ix + -3ix2 + 32x + -4x2 + -1x3)(3i + -1x) = 0 (96i + -12ix + -3ix2 + 32x + -4x2 + -1x3)(3i + -1x) = 0 Multiply (96i + -12ix + -3ix2 + 32x + -4x2 + -1x3) * (3i + -1x) (96i * (3i + -1x) + -12ix * (3i + -1x) + -3ix2 * (3i + -1x) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 ((3i * 96i + -1x * 96i) + -12ix * (3i + -1x) + -3ix2 * (3i + -1x) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 Reorder the terms: ((-96ix + 288i2) + -12ix * (3i + -1x) + -3ix2 * (3i + -1x) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 ((-96ix + 288i2) + -12ix * (3i + -1x) + -3ix2 * (3i + -1x) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + (3i * -12ix + -1x * -12ix) + -3ix2 * (3i + -1x) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 Reorder the terms: (-96ix + 288i2 + (12ix2 + -36i2x) + -3ix2 * (3i + -1x) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + (12ix2 + -36i2x) + -3ix2 * (3i + -1x) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + 12ix2 + -36i2x + (3i * -3ix2 + -1x * -3ix2) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 Reorder the terms: (-96ix + 288i2 + 12ix2 + -36i2x + (3ix3 + -9i2x2) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + 12ix2 + -36i2x + (3ix3 + -9i2x2) + 32x * (3i + -1x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + 12ix2 + -36i2x + 3ix3 + -9i2x2 + (3i * 32x + -1x * 32x) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + 12ix2 + -36i2x + 3ix3 + -9i2x2 + (96ix + -32x2) + -4x2 * (3i + -1x) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + 12ix2 + -36i2x + 3ix3 + -9i2x2 + 96ix + -32x2 + (3i * -4x2 + -1x * -4x2) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + 12ix2 + -36i2x + 3ix3 + -9i2x2 + 96ix + -32x2 + (-12ix2 + 4x3) + -1x3 * (3i + -1x)) = 0 (-96ix + 288i2 + 12ix2 + -36i2x + 3ix3 + -9i2x2 + 96ix + -32x2 + -12ix2 + 4x3 + (3i * -1x3 + -1x * -1x3)) = 0 (-96ix + 288i2 + 12ix2 + -36i2x + 3ix3 + -9i2x2 + 96ix + -32x2 + -12ix2 + 4x3 + (-3ix3 + 1x4)) = 0 Reorder the terms: (-96ix + 96ix + 12ix2 + -12ix2 + 3ix3 + -3ix3 + 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 1x4) = 0 Combine like terms: -96ix + 96ix = 0 (0 + 12ix2 + -12ix2 + 3ix3 + -3ix3 + 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 1x4) = 0 (12ix2 + -12ix2 + 3ix3 + -3ix3 + 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 1x4) = 0 Combine like terms: 12ix2 + -12ix2 = 0 (0 + 3ix3 + -3ix3 + 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 1x4) = 0 (3ix3 + -3ix3 + 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 1x4) = 0 Combine like terms: 3ix3 + -3ix3 = 0 (0 + 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 1x4) = 0 (288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 1x4) = 0 Solving 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 1x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '32x2' to each side of the equation. 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + 32x2 + 1x4 = 0 + 32x2 Reorder the terms: 288i2 + -36i2x + -9i2x2 + -32x2 + 32x2 + 4x3 + 1x4 = 0 + 32x2 Combine like terms: -32x2 + 32x2 = 0 288i2 + -36i2x + -9i2x2 + 0 + 4x3 + 1x4 = 0 + 32x2 288i2 + -36i2x + -9i2x2 + 4x3 + 1x4 = 0 + 32x2 Remove the zero: 288i2 + -36i2x + -9i2x2 + 4x3 + 1x4 = 32x2 Add '-4x3' to each side of the equation. 288i2 + -36i2x + -9i2x2 + 4x3 + -4x3 + 1x4 = 32x2 + -4x3 Combine like terms: 4x3 + -4x3 = 0 288i2 + -36i2x + -9i2x2 + 0 + 1x4 = 32x2 + -4x3 288i2 + -36i2x + -9i2x2 + 1x4 = 32x2 + -4x3 Add '-1x4' to each side of the equation. 288i2 + -36i2x + -9i2x2 + 1x4 + -1x4 = 32x2 + -4x3 + -1x4 Combine like terms: 1x4 + -1x4 = 0 288i2 + -36i2x + -9i2x2 + 0 = 32x2 + -4x3 + -1x4 288i2 + -36i2x + -9i2x2 = 32x2 + -4x3 + -1x4 Reorder the terms: 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + x4 = 32x2 + -32x2 + -4x3 + 4x3 + -1x4 + x4 Combine like terms: 32x2 + -32x2 = 0 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + x4 = 0 + -4x3 + 4x3 + -1x4 + x4 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + x4 = -4x3 + 4x3 + -1x4 + x4 Combine like terms: -4x3 + 4x3 = 0 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + x4 = 0 + -1x4 + x4 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 288i2 + -36i2x + -9i2x2 + -32x2 + 4x3 + x4 = 0 The solution to this equation could not be determined.
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