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Simplifying (x + 3)(x + -8 + -4i)(x + -8 + 4i) = 0 Reorder the terms: (3 + x)(x + -8 + -4i)(x + -8 + 4i) = 0 Reorder the terms: (3 + x)(-8 + -4i + x)(x + -8 + 4i) = 0 Reorder the terms: (3 + x)(-8 + -4i + x)(-8 + 4i + x) = 0 Multiply (3 + x) * (-8 + -4i + x) (3(-8 + -4i + x) + x(-8 + -4i + x))(-8 + 4i + x) = 0 ((-8 * 3 + -4i * 3 + x * 3) + x(-8 + -4i + x))(-8 + 4i + x) = 0 ((-24 + -12i + 3x) + x(-8 + -4i + x))(-8 + 4i + x) = 0 (-24 + -12i + 3x + (-8 * x + -4i * x + x * x))(-8 + 4i + x) = 0 Reorder the terms: (-24 + -12i + 3x + (-4ix + -8x + x2))(-8 + 4i + x) = 0 (-24 + -12i + 3x + (-4ix + -8x + x2))(-8 + 4i + x) = 0 Reorder the terms: (-24 + -12i + -4ix + 3x + -8x + x2)(-8 + 4i + x) = 0 Combine like terms: 3x + -8x = -5x (-24 + -12i + -4ix + -5x + x2)(-8 + 4i + x) = 0 Multiply (-24 + -12i + -4ix + -5x + x2) * (-8 + 4i + x) (-24(-8 + 4i + x) + -12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 ((-8 * -24 + 4i * -24 + x * -24) + -12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 ((192 + -96i + -24x) + -12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 (192 + -96i + -24x + (-8 * -12i + 4i * -12i + x * -12i) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 Reorder the terms: (192 + -96i + -24x + (96i + -12ix + -48i2) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 (192 + -96i + -24x + (96i + -12ix + -48i2) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 (192 + -96i + -24x + 96i + -12ix + -48i2 + (-8 * -4ix + 4i * -4ix + x * -4ix) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 Reorder the terms: (192 + -96i + -24x + 96i + -12ix + -48i2 + (32ix + -4ix2 + -16i2x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 (192 + -96i + -24x + 96i + -12ix + -48i2 + (32ix + -4ix2 + -16i2x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x)) = 0 (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + (-8 * -5x + 4i * -5x + x * -5x) + x2(-8 + 4i + x)) = 0 Reorder the terms: (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + (-20ix + 40x + -5x2) + x2(-8 + 4i + x)) = 0 (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + (-20ix + 40x + -5x2) + x2(-8 + 4i + x)) = 0 (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + -20ix + 40x + -5x2 + (-8 * x2 + 4i * x2 + x * x2)) = 0 Reorder the terms: (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + -20ix + 40x + -5x2 + (4ix2 + -8x2 + x3)) = 0 (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + -20ix + 40x + -5x2 + (4ix2 + -8x2 + x3)) = 0 Reorder the terms: (192 + -96i + 96i + -12ix + 32ix + -20ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3) = 0 Combine like terms: -96i + 96i = 0 (192 + 0 + -12ix + 32ix + -20ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3) = 0 (192 + -12ix + 32ix + -20ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3) = 0 Combine like terms: -12ix + 32ix = 20ix (192 + 20ix + -20ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3) = 0 Combine like terms: 20ix + -20ix = 0 (192 + 0 + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3) = 0 (192 + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3) = 0 Combine like terms: -4ix2 + 4ix2 = 0 (192 + 0 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3) = 0 (192 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3) = 0 Combine like terms: -24x + 40x = 16x (192 + -48i2 + -16i2x + 16x + -5x2 + -8x2 + x3) = 0 Combine like terms: -5x2 + -8x2 = -13x2 (192 + -48i2 + -16i2x + 16x + -13x2 + x3) = 0 Solving 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-192' to each side of the equation. 192 + -48i2 + -16i2x + 16x + -13x2 + -192 + x3 = 0 + -192 Reorder the terms: 192 + -192 + -48i2 + -16i2x + 16x + -13x2 + x3 = 0 + -192 Combine like terms: 192 + -192 = 0 0 + -48i2 + -16i2x + 16x + -13x2 + x3 = 0 + -192 -48i2 + -16i2x + 16x + -13x2 + x3 = 0 + -192 Combine like terms: 0 + -192 = -192 -48i2 + -16i2x + 16x + -13x2 + x3 = -192 Add '-16x' to each side of the equation. -48i2 + -16i2x + 16x + -13x2 + -16x + x3 = -192 + -16x Reorder the terms: -48i2 + -16i2x + 16x + -16x + -13x2 + x3 = -192 + -16x Combine like terms: 16x + -16x = 0 -48i2 + -16i2x + 0 + -13x2 + x3 = -192 + -16x -48i2 + -16i2x + -13x2 + x3 = -192 + -16x Add '13x2' to each side of the equation. -48i2 + -16i2x + -13x2 + 13x2 + x3 = -192 + -16x + 13x2 Combine like terms: -13x2 + 13x2 = 0 -48i2 + -16i2x + 0 + x3 = -192 + -16x + 13x2 -48i2 + -16i2x + x3 = -192 + -16x + 13x2 Add '-1x3' to each side of the equation. -48i2 + -16i2x + x3 + -1x3 = -192 + -16x + 13x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -48i2 + -16i2x + 0 = -192 + -16x + 13x2 + -1x3 -48i2 + -16i2x = -192 + -16x + 13x2 + -1x3 Reorder the terms: 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = -192 + -16x + 13x2 + -1x3 + 192 + 16x + -13x2 + x3 Reorder the terms: 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = -192 + 192 + -16x + 16x + 13x2 + -13x2 + -1x3 + x3 Combine like terms: -192 + 192 = 0 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = 0 + -16x + 16x + 13x2 + -13x2 + -1x3 + x3 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = -16x + 16x + 13x2 + -13x2 + -1x3 + x3 Combine like terms: -16x + 16x = 0 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = 0 + 13x2 + -13x2 + -1x3 + x3 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = 13x2 + -13x2 + -1x3 + x3 Combine like terms: 13x2 + -13x2 = 0 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = 0 + -1x3 + x3 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 192 + -48i2 + -16i2x + 16x + -13x2 + x3 = 0 The solution to this equation could not be determined.
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