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Simplifying (x + 4)(x + -8)(x + -2 + 3i)(x + -2 + -3i) = 0 Reorder the terms: (4 + x)(x + -8)(x + -2 + 3i)(x + -2 + -3i) = 0 Reorder the terms: (4 + x)(-8 + x)(x + -2 + 3i)(x + -2 + -3i) = 0 Reorder the terms: (4 + x)(-8 + x)(-2 + 3i + x)(x + -2 + -3i) = 0 Reorder the terms: (4 + x)(-8 + x)(-2 + 3i + x)(-2 + -3i + x) = 0 Multiply (4 + x) * (-8 + x) (4(-8 + x) + x(-8 + x))(-2 + 3i + x)(-2 + -3i + x) = 0 ((-8 * 4 + x * 4) + x(-8 + x))(-2 + 3i + x)(-2 + -3i + x) = 0 ((-32 + 4x) + x(-8 + x))(-2 + 3i + x)(-2 + -3i + x) = 0 (-32 + 4x + (-8 * x + x * x))(-2 + 3i + x)(-2 + -3i + x) = 0 (-32 + 4x + (-8x + x2))(-2 + 3i + x)(-2 + -3i + x) = 0 Combine like terms: 4x + -8x = -4x (-32 + -4x + x2)(-2 + 3i + x)(-2 + -3i + x) = 0 Multiply (-32 + -4x + x2) * (-2 + 3i + x) (-32(-2 + 3i + x) + -4x * (-2 + 3i + x) + x2(-2 + 3i + x))(-2 + -3i + x) = 0 ((-2 * -32 + 3i * -32 + x * -32) + -4x * (-2 + 3i + x) + x2(-2 + 3i + x))(-2 + -3i + x) = 0 ((64 + -96i + -32x) + -4x * (-2 + 3i + x) + x2(-2 + 3i + x))(-2 + -3i + x) = 0 (64 + -96i + -32x + (-2 * -4x + 3i * -4x + x * -4x) + x2(-2 + 3i + x))(-2 + -3i + x) = 0 Reorder the terms: (64 + -96i + -32x + (-12ix + 8x + -4x2) + x2(-2 + 3i + x))(-2 + -3i + x) = 0 (64 + -96i + -32x + (-12ix + 8x + -4x2) + x2(-2 + 3i + x))(-2 + -3i + x) = 0 (64 + -96i + -32x + -12ix + 8x + -4x2 + (-2 * x2 + 3i * x2 + x * x2))(-2 + -3i + x) = 0 Reorder the terms: (64 + -96i + -32x + -12ix + 8x + -4x2 + (3ix2 + -2x2 + x3))(-2 + -3i + x) = 0 (64 + -96i + -32x + -12ix + 8x + -4x2 + (3ix2 + -2x2 + x3))(-2 + -3i + x) = 0 Reorder the terms: (64 + -96i + -12ix + 3ix2 + -32x + 8x + -4x2 + -2x2 + x3)(-2 + -3i + x) = 0 Combine like terms: -32x + 8x = -24x (64 + -96i + -12ix + 3ix2 + -24x + -4x2 + -2x2 + x3)(-2 + -3i + x) = 0 Combine like terms: -4x2 + -2x2 = -6x2 (64 + -96i + -12ix + 3ix2 + -24x + -6x2 + x3)(-2 + -3i + x) = 0 Multiply (64 + -96i + -12ix + 3ix2 + -24x + -6x2 + x3) * (-2 + -3i + x) (64(-2 + -3i + x) + -96i * (-2 + -3i + x) + -12ix * (-2 + -3i + x) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 ((-2 * 64 + -3i * 64 + x * 64) + -96i * (-2 + -3i + x) + -12ix * (-2 + -3i + x) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 ((-128 + -192i + 64x) + -96i * (-2 + -3i + x) + -12ix * (-2 + -3i + x) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + (-2 * -96i + -3i * -96i + x * -96i) + -12ix * (-2 + -3i + x) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 Reorder the terms: (-128 + -192i + 64x + (192i + -96ix + 288i2) + -12ix * (-2 + -3i + x) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + (192i + -96ix + 288i2) + -12ix * (-2 + -3i + x) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + (-2 * -12ix + -3i * -12ix + x * -12ix) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 Reorder the terms: (-128 + -192i + 64x + 192i + -96ix + 288i2 + (24ix + -12ix2 + 36i2x) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + (24ix + -12ix2 + 36i2x) + 3ix2 * (-2 + -3i + x) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + (-2 * 3ix2 + -3i * 3ix2 + x * 3ix2) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 Reorder the terms: (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + (-6ix2 + 3ix3 + -9i2x2) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + (-6ix2 + 3ix3 + -9i2x2) + -24x * (-2 + -3i + x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + (-2 * -24x + -3i * -24x + x * -24x) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 Reorder the terms: (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + (72ix + 48x + -24x2) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + (72ix + 48x + -24x2) + -6x2 * (-2 + -3i + x) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + 72ix + 48x + -24x2 + (-2 * -6x2 + -3i * -6x2 + x * -6x2) + x3(-2 + -3i + x)) = 0 Reorder the terms: (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + 72ix + 48x + -24x2 + (18ix2 + 12x2 + -6x3) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + 72ix + 48x + -24x2 + (18ix2 + 12x2 + -6x3) + x3(-2 + -3i + x)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + 72ix + 48x + -24x2 + 18ix2 + 12x2 + -6x3 + (-2 * x3 + -3i * x3 + x * x3)) = 0 Reorder the terms: (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + 72ix + 48x + -24x2 + 18ix2 + 12x2 + -6x3 + (-3ix3 + -2x3 + x4)) = 0 (-128 + -192i + 64x + 192i + -96ix + 288i2 + 24ix + -12ix2 + 36i2x + -6ix2 + 3ix3 + -9i2x2 + 72ix + 48x + -24x2 + 18ix2 + 12x2 + -6x3 + (-3ix3 + -2x3 + x4)) = 0 Reorder the terms: (-128 + -192i + 192i + -96ix + 24ix + 72ix + -12ix2 + -6ix2 + 18ix2 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: -192i + 192i = 0 (-128 + 0 + -96ix + 24ix + 72ix + -12ix2 + -6ix2 + 18ix2 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 (-128 + -96ix + 24ix + 72ix + -12ix2 + -6ix2 + 18ix2 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: -96ix + 24ix = -72ix (-128 + -72ix + 72ix + -12ix2 + -6ix2 + 18ix2 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: -72ix + 72ix = 0 (-128 + 0 + -12ix2 + -6ix2 + 18ix2 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 (-128 + -12ix2 + -6ix2 + 18ix2 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: -12ix2 + -6ix2 = -18ix2 (-128 + -18ix2 + 18ix2 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: -18ix2 + 18ix2 = 0 (-128 + 0 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 (-128 + 3ix3 + -3ix3 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: 3ix3 + -3ix3 = 0 (-128 + 0 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 (-128 + 288i2 + 36i2x + -9i2x2 + 64x + 48x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: 64x + 48x = 112x (-128 + 288i2 + 36i2x + -9i2x2 + 112x + -24x2 + 12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: -24x2 + 12x2 = -12x2 (-128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -6x3 + -2x3 + x4) = 0 Combine like terms: -6x3 + -2x3 = -8x3 (-128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4) = 0 Solving -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '128' to each side of the equation. -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + 128 + x4 = 0 + 128 Reorder the terms: -128 + 128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 + 128 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 + 128 Combine like terms: 0 + 128 = 128 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 128 Add '-112x' to each side of the equation. 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + -112x + x4 = 128 + -112x Reorder the terms: 288i2 + 36i2x + -9i2x2 + 112x + -112x + -12x2 + -8x3 + x4 = 128 + -112x Combine like terms: 112x + -112x = 0 288i2 + 36i2x + -9i2x2 + 0 + -12x2 + -8x3 + x4 = 128 + -112x 288i2 + 36i2x + -9i2x2 + -12x2 + -8x3 + x4 = 128 + -112x Add '12x2' to each side of the equation. 288i2 + 36i2x + -9i2x2 + -12x2 + -8x3 + 12x2 + x4 = 128 + -112x + 12x2 Reorder the terms: 288i2 + 36i2x + -9i2x2 + -12x2 + 12x2 + -8x3 + x4 = 128 + -112x + 12x2 Combine like terms: -12x2 + 12x2 = 0 288i2 + 36i2x + -9i2x2 + 0 + -8x3 + x4 = 128 + -112x + 12x2 288i2 + 36i2x + -9i2x2 + -8x3 + x4 = 128 + -112x + 12x2 Add '8x3' to each side of the equation. 288i2 + 36i2x + -9i2x2 + -8x3 + 8x3 + x4 = 128 + -112x + 12x2 + 8x3 Combine like terms: -8x3 + 8x3 = 0 288i2 + 36i2x + -9i2x2 + 0 + x4 = 128 + -112x + 12x2 + 8x3 288i2 + 36i2x + -9i2x2 + x4 = 128 + -112x + 12x2 + 8x3 Add '-1x4' to each side of the equation. 288i2 + 36i2x + -9i2x2 + x4 + -1x4 = 128 + -112x + 12x2 + 8x3 + -1x4 Combine like terms: x4 + -1x4 = 0 288i2 + 36i2x + -9i2x2 + 0 = 128 + -112x + 12x2 + 8x3 + -1x4 288i2 + 36i2x + -9i2x2 = 128 + -112x + 12x2 + 8x3 + -1x4 Reorder the terms: -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 128 + -112x + 12x2 + 8x3 + -1x4 + -128 + 112x + -12x2 + -8x3 + x4 Reorder the terms: -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 128 + -128 + -112x + 112x + 12x2 + -12x2 + 8x3 + -8x3 + -1x4 + x4 Combine like terms: 128 + -128 = 0 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 + -112x + 112x + 12x2 + -12x2 + 8x3 + -8x3 + -1x4 + x4 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = -112x + 112x + 12x2 + -12x2 + 8x3 + -8x3 + -1x4 + x4 Combine like terms: -112x + 112x = 0 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 + 12x2 + -12x2 + 8x3 + -8x3 + -1x4 + x4 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 12x2 + -12x2 + 8x3 + -8x3 + -1x4 + x4 Combine like terms: 12x2 + -12x2 = 0 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 + 8x3 + -8x3 + -1x4 + x4 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 8x3 + -8x3 + -1x4 + x4 Combine like terms: 8x3 + -8x3 = 0 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 + -1x4 + x4 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -128 + 288i2 + 36i2x + -9i2x2 + 112x + -12x2 + -8x3 + x4 = 0 The solution to this equation could not be determined.
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