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Simplifying (x + -2)(x + -1(6 + 7i))(x + -1(6 + -7i)) = 0 Reorder the terms: (-2 + x)(x + -1(6 + 7i))(x + -1(6 + -7i)) = 0 (-2 + x)(x + (6 * -1 + 7i * -1))(x + -1(6 + -7i)) = 0 (-2 + x)(x + (-6 + -7i))(x + -1(6 + -7i)) = 0 Reorder the terms: (-2 + x)(-6 + -7i + x)(x + -1(6 + -7i)) = 0 (-2 + x)(-6 + -7i + x)(x + (6 * -1 + -7i * -1)) = 0 (-2 + x)(-6 + -7i + x)(x + (-6 + 7i)) = 0 Reorder the terms: (-2 + x)(-6 + -7i + x)(-6 + 7i + x) = 0 Multiply (-2 + x) * (-6 + -7i + x) (-2(-6 + -7i + x) + x(-6 + -7i + x))(-6 + 7i + x) = 0 ((-6 * -2 + -7i * -2 + x * -2) + x(-6 + -7i + x))(-6 + 7i + x) = 0 ((12 + 14i + -2x) + x(-6 + -7i + x))(-6 + 7i + x) = 0 (12 + 14i + -2x + (-6 * x + -7i * x + x * x))(-6 + 7i + x) = 0 Reorder the terms: (12 + 14i + -2x + (-7ix + -6x + x2))(-6 + 7i + x) = 0 (12 + 14i + -2x + (-7ix + -6x + x2))(-6 + 7i + x) = 0 Reorder the terms: (12 + 14i + -7ix + -2x + -6x + x2)(-6 + 7i + x) = 0 Combine like terms: -2x + -6x = -8x (12 + 14i + -7ix + -8x + x2)(-6 + 7i + x) = 0 Multiply (12 + 14i + -7ix + -8x + x2) * (-6 + 7i + x) (12(-6 + 7i + x) + 14i * (-6 + 7i + x) + -7ix * (-6 + 7i + x) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 ((-6 * 12 + 7i * 12 + x * 12) + 14i * (-6 + 7i + x) + -7ix * (-6 + 7i + x) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 ((-72 + 84i + 12x) + 14i * (-6 + 7i + x) + -7ix * (-6 + 7i + x) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 (-72 + 84i + 12x + (-6 * 14i + 7i * 14i + x * 14i) + -7ix * (-6 + 7i + x) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 Reorder the terms: (-72 + 84i + 12x + (-84i + 14ix + 98i2) + -7ix * (-6 + 7i + x) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 (-72 + 84i + 12x + (-84i + 14ix + 98i2) + -7ix * (-6 + 7i + x) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 (-72 + 84i + 12x + -84i + 14ix + 98i2 + (-6 * -7ix + 7i * -7ix + x * -7ix) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 Reorder the terms: (-72 + 84i + 12x + -84i + 14ix + 98i2 + (42ix + -7ix2 + -49i2x) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 (-72 + 84i + 12x + -84i + 14ix + 98i2 + (42ix + -7ix2 + -49i2x) + -8x * (-6 + 7i + x) + x2(-6 + 7i + x)) = 0 (-72 + 84i + 12x + -84i + 14ix + 98i2 + 42ix + -7ix2 + -49i2x + (-6 * -8x + 7i * -8x + x * -8x) + x2(-6 + 7i + x)) = 0 Reorder the terms: (-72 + 84i + 12x + -84i + 14ix + 98i2 + 42ix + -7ix2 + -49i2x + (-56ix + 48x + -8x2) + x2(-6 + 7i + x)) = 0 (-72 + 84i + 12x + -84i + 14ix + 98i2 + 42ix + -7ix2 + -49i2x + (-56ix + 48x + -8x2) + x2(-6 + 7i + x)) = 0 (-72 + 84i + 12x + -84i + 14ix + 98i2 + 42ix + -7ix2 + -49i2x + -56ix + 48x + -8x2 + (-6 * x2 + 7i * x2 + x * x2)) = 0 Reorder the terms: (-72 + 84i + 12x + -84i + 14ix + 98i2 + 42ix + -7ix2 + -49i2x + -56ix + 48x + -8x2 + (7ix2 + -6x2 + x3)) = 0 (-72 + 84i + 12x + -84i + 14ix + 98i2 + 42ix + -7ix2 + -49i2x + -56ix + 48x + -8x2 + (7ix2 + -6x2 + x3)) = 0 Reorder the terms: (-72 + 84i + -84i + 14ix + 42ix + -56ix + -7ix2 + 7ix2 + 98i2 + -49i2x + 12x + 48x + -8x2 + -6x2 + x3) = 0 Combine like terms: 84i + -84i = 0 (-72 + 0 + 14ix + 42ix + -56ix + -7ix2 + 7ix2 + 98i2 + -49i2x + 12x + 48x + -8x2 + -6x2 + x3) = 0 (-72 + 14ix + 42ix + -56ix + -7ix2 + 7ix2 + 98i2 + -49i2x + 12x + 48x + -8x2 + -6x2 + x3) = 0 Combine like terms: 14ix + 42ix = 56ix (-72 + 56ix + -56ix + -7ix2 + 7ix2 + 98i2 + -49i2x + 12x + 48x + -8x2 + -6x2 + x3) = 0 Combine like terms: 56ix + -56ix = 0 (-72 + 0 + -7ix2 + 7ix2 + 98i2 + -49i2x + 12x + 48x + -8x2 + -6x2 + x3) = 0 (-72 + -7ix2 + 7ix2 + 98i2 + -49i2x + 12x + 48x + -8x2 + -6x2 + x3) = 0 Combine like terms: -7ix2 + 7ix2 = 0 (-72 + 0 + 98i2 + -49i2x + 12x + 48x + -8x2 + -6x2 + x3) = 0 (-72 + 98i2 + -49i2x + 12x + 48x + -8x2 + -6x2 + x3) = 0 Combine like terms: 12x + 48x = 60x (-72 + 98i2 + -49i2x + 60x + -8x2 + -6x2 + x3) = 0 Combine like terms: -8x2 + -6x2 = -14x2 (-72 + 98i2 + -49i2x + 60x + -14x2 + x3) = 0 Solving -72 + 98i2 + -49i2x + 60x + -14x2 + 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 + 98i2 + -49i2x + 60x + -14x2 + 72 + x3 = 0 + 72 Reorder the terms: -72 + 72 + 98i2 + -49i2x + 60x + -14x2 + x3 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 98i2 + -49i2x + 60x + -14x2 + x3 = 0 + 72 98i2 + -49i2x + 60x + -14x2 + x3 = 0 + 72 Combine like terms: 0 + 72 = 72 98i2 + -49i2x + 60x + -14x2 + x3 = 72 Add '-60x' to each side of the equation. 98i2 + -49i2x + 60x + -14x2 + -60x + x3 = 72 + -60x Reorder the terms: 98i2 + -49i2x + 60x + -60x + -14x2 + x3 = 72 + -60x Combine like terms: 60x + -60x = 0 98i2 + -49i2x + 0 + -14x2 + x3 = 72 + -60x 98i2 + -49i2x + -14x2 + x3 = 72 + -60x Add '14x2' to each side of the equation. 98i2 + -49i2x + -14x2 + 14x2 + x3 = 72 + -60x + 14x2 Combine like terms: -14x2 + 14x2 = 0 98i2 + -49i2x + 0 + x3 = 72 + -60x + 14x2 98i2 + -49i2x + x3 = 72 + -60x + 14x2 Add '-1x3' to each side of the equation. 98i2 + -49i2x + x3 + -1x3 = 72 + -60x + 14x2 + -1x3 Combine like terms: x3 + -1x3 = 0 98i2 + -49i2x + 0 = 72 + -60x + 14x2 + -1x3 98i2 + -49i2x = 72 + -60x + 14x2 + -1x3 Reorder the terms: -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = 72 + -60x + 14x2 + -1x3 + -72 + 60x + -14x2 + x3 Reorder the terms: -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = 72 + -72 + -60x + 60x + 14x2 + -14x2 + -1x3 + x3 Combine like terms: 72 + -72 = 0 -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = 0 + -60x + 60x + 14x2 + -14x2 + -1x3 + x3 -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = -60x + 60x + 14x2 + -14x2 + -1x3 + x3 Combine like terms: -60x + 60x = 0 -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = 0 + 14x2 + -14x2 + -1x3 + x3 -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = 14x2 + -14x2 + -1x3 + x3 Combine like terms: 14x2 + -14x2 = 0 -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = 0 + -1x3 + x3 -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -72 + 98i2 + -49i2x + 60x + -14x2 + x3 = 0 The solution to this equation could not be determined.
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