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Simplifying (x + 2)(x + -6 + -2i)(x + -6 + 2i) = 0 Reorder the terms: (2 + x)(x + -6 + -2i)(x + -6 + 2i) = 0 Reorder the terms: (2 + x)(-6 + -2i + x)(x + -6 + 2i) = 0 Reorder the terms: (2 + x)(-6 + -2i + x)(-6 + 2i + x) = 0 Multiply (2 + x) * (-6 + -2i + x) (2(-6 + -2i + x) + x(-6 + -2i + x))(-6 + 2i + x) = 0 ((-6 * 2 + -2i * 2 + x * 2) + x(-6 + -2i + x))(-6 + 2i + x) = 0 ((-12 + -4i + 2x) + x(-6 + -2i + x))(-6 + 2i + x) = 0 (-12 + -4i + 2x + (-6 * x + -2i * x + x * x))(-6 + 2i + x) = 0 Reorder the terms: (-12 + -4i + 2x + (-2ix + -6x + x2))(-6 + 2i + x) = 0 (-12 + -4i + 2x + (-2ix + -6x + x2))(-6 + 2i + x) = 0 Reorder the terms: (-12 + -4i + -2ix + 2x + -6x + x2)(-6 + 2i + x) = 0 Combine like terms: 2x + -6x = -4x (-12 + -4i + -2ix + -4x + x2)(-6 + 2i + x) = 0 Multiply (-12 + -4i + -2ix + -4x + x2) * (-6 + 2i + x) (-12(-6 + 2i + x) + -4i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 ((-6 * -12 + 2i * -12 + x * -12) + -4i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 ((72 + -24i + -12x) + -4i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 (72 + -24i + -12x + (-6 * -4i + 2i * -4i + x * -4i) + -2ix * (-6 + 2i + x) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 Reorder the terms: (72 + -24i + -12x + (24i + -4ix + -8i2) + -2ix * (-6 + 2i + x) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 (72 + -24i + -12x + (24i + -4ix + -8i2) + -2ix * (-6 + 2i + x) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 (72 + -24i + -12x + 24i + -4ix + -8i2 + (-6 * -2ix + 2i * -2ix + x * -2ix) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 Reorder the terms: (72 + -24i + -12x + 24i + -4ix + -8i2 + (12ix + -2ix2 + -4i2x) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 (72 + -24i + -12x + 24i + -4ix + -8i2 + (12ix + -2ix2 + -4i2x) + -4x * (-6 + 2i + x) + x2(-6 + 2i + x)) = 0 (72 + -24i + -12x + 24i + -4ix + -8i2 + 12ix + -2ix2 + -4i2x + (-6 * -4x + 2i * -4x + x * -4x) + x2(-6 + 2i + x)) = 0 Reorder the terms: (72 + -24i + -12x + 24i + -4ix + -8i2 + 12ix + -2ix2 + -4i2x + (-8ix + 24x + -4x2) + x2(-6 + 2i + x)) = 0 (72 + -24i + -12x + 24i + -4ix + -8i2 + 12ix + -2ix2 + -4i2x + (-8ix + 24x + -4x2) + x2(-6 + 2i + x)) = 0 (72 + -24i + -12x + 24i + -4ix + -8i2 + 12ix + -2ix2 + -4i2x + -8ix + 24x + -4x2 + (-6 * x2 + 2i * x2 + x * x2)) = 0 Reorder the terms: (72 + -24i + -12x + 24i + -4ix + -8i2 + 12ix + -2ix2 + -4i2x + -8ix + 24x + -4x2 + (2ix2 + -6x2 + x3)) = 0 (72 + -24i + -12x + 24i + -4ix + -8i2 + 12ix + -2ix2 + -4i2x + -8ix + 24x + -4x2 + (2ix2 + -6x2 + x3)) = 0 Reorder the terms: (72 + -24i + 24i + -4ix + 12ix + -8ix + -2ix2 + 2ix2 + -8i2 + -4i2x + -12x + 24x + -4x2 + -6x2 + x3) = 0 Combine like terms: -24i + 24i = 0 (72 + 0 + -4ix + 12ix + -8ix + -2ix2 + 2ix2 + -8i2 + -4i2x + -12x + 24x + -4x2 + -6x2 + x3) = 0 (72 + -4ix + 12ix + -8ix + -2ix2 + 2ix2 + -8i2 + -4i2x + -12x + 24x + -4x2 + -6x2 + x3) = 0 Combine like terms: -4ix + 12ix = 8ix (72 + 8ix + -8ix + -2ix2 + 2ix2 + -8i2 + -4i2x + -12x + 24x + -4x2 + -6x2 + x3) = 0 Combine like terms: 8ix + -8ix = 0 (72 + 0 + -2ix2 + 2ix2 + -8i2 + -4i2x + -12x + 24x + -4x2 + -6x2 + x3) = 0 (72 + -2ix2 + 2ix2 + -8i2 + -4i2x + -12x + 24x + -4x2 + -6x2 + x3) = 0 Combine like terms: -2ix2 + 2ix2 = 0 (72 + 0 + -8i2 + -4i2x + -12x + 24x + -4x2 + -6x2 + x3) = 0 (72 + -8i2 + -4i2x + -12x + 24x + -4x2 + -6x2 + x3) = 0 Combine like terms: -12x + 24x = 12x (72 + -8i2 + -4i2x + 12x + -4x2 + -6x2 + x3) = 0 Combine like terms: -4x2 + -6x2 = -10x2 (72 + -8i2 + -4i2x + 12x + -10x2 + x3) = 0 Solving 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-72' to each side of the equation. 72 + -8i2 + -4i2x + 12x + -10x2 + -72 + x3 = 0 + -72 Reorder the terms: 72 + -72 + -8i2 + -4i2x + 12x + -10x2 + x3 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -8i2 + -4i2x + 12x + -10x2 + x3 = 0 + -72 -8i2 + -4i2x + 12x + -10x2 + x3 = 0 + -72 Combine like terms: 0 + -72 = -72 -8i2 + -4i2x + 12x + -10x2 + x3 = -72 Add '-12x' to each side of the equation. -8i2 + -4i2x + 12x + -10x2 + -12x + x3 = -72 + -12x Reorder the terms: -8i2 + -4i2x + 12x + -12x + -10x2 + x3 = -72 + -12x Combine like terms: 12x + -12x = 0 -8i2 + -4i2x + 0 + -10x2 + x3 = -72 + -12x -8i2 + -4i2x + -10x2 + x3 = -72 + -12x Add '10x2' to each side of the equation. -8i2 + -4i2x + -10x2 + 10x2 + x3 = -72 + -12x + 10x2 Combine like terms: -10x2 + 10x2 = 0 -8i2 + -4i2x + 0 + x3 = -72 + -12x + 10x2 -8i2 + -4i2x + x3 = -72 + -12x + 10x2 Add '-1x3' to each side of the equation. -8i2 + -4i2x + x3 + -1x3 = -72 + -12x + 10x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -8i2 + -4i2x + 0 = -72 + -12x + 10x2 + -1x3 -8i2 + -4i2x = -72 + -12x + 10x2 + -1x3 Reorder the terms: 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = -72 + -12x + 10x2 + -1x3 + 72 + 12x + -10x2 + x3 Reorder the terms: 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = -72 + 72 + -12x + 12x + 10x2 + -10x2 + -1x3 + x3 Combine like terms: -72 + 72 = 0 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = 0 + -12x + 12x + 10x2 + -10x2 + -1x3 + x3 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = -12x + 12x + 10x2 + -10x2 + -1x3 + x3 Combine like terms: -12x + 12x = 0 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = 0 + 10x2 + -10x2 + -1x3 + x3 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = 10x2 + -10x2 + -1x3 + x3 Combine like terms: 10x2 + -10x2 = 0 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = 0 + -1x3 + x3 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 72 + -8i2 + -4i2x + 12x + -10x2 + x3 = 0 The solution to this equation could not be determined.
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