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Simplifying (x + -6)(x + -1 + -1i)(x + -1 + i) = 0 Reorder the terms: (-6 + x)(x + -1 + -1i)(x + -1 + i) = 0 Reorder the terms: (-6 + x)(-1 + -1i + x)(x + -1 + i) = 0 Reorder the terms: (-6 + x)(-1 + -1i + x)(-1 + i + x) = 0 Multiply (-6 + x) * (-1 + -1i + x) (-6(-1 + -1i + x) + x(-1 + -1i + x))(-1 + i + x) = 0 ((-1 * -6 + -1i * -6 + x * -6) + x(-1 + -1i + x))(-1 + i + x) = 0 ((6 + 6i + -6x) + x(-1 + -1i + x))(-1 + i + x) = 0 (6 + 6i + -6x + (-1 * x + -1i * x + x * x))(-1 + i + x) = 0 Reorder the terms: (6 + 6i + -6x + (-1ix + -1x + x2))(-1 + i + x) = 0 (6 + 6i + -6x + (-1ix + -1x + x2))(-1 + i + x) = 0 Reorder the terms: (6 + 6i + -1ix + -6x + -1x + x2)(-1 + i + x) = 0 Combine like terms: -6x + -1x = -7x (6 + 6i + -1ix + -7x + x2)(-1 + i + x) = 0 Multiply (6 + 6i + -1ix + -7x + x2) * (-1 + i + x) (6(-1 + i + x) + 6i * (-1 + i + x) + -1ix * (-1 + i + x) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 ((-1 * 6 + i * 6 + x * 6) + 6i * (-1 + i + x) + -1ix * (-1 + i + x) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 ((-6 + 6i + 6x) + 6i * (-1 + i + x) + -1ix * (-1 + i + x) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-6 + 6i + 6x + (-1 * 6i + i * 6i + x * 6i) + -1ix * (-1 + i + x) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 Reorder the terms: (-6 + 6i + 6x + (-6i + 6ix + 6i2) + -1ix * (-1 + i + x) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-6 + 6i + 6x + (-6i + 6ix + 6i2) + -1ix * (-1 + i + x) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-6 + 6i + 6x + -6i + 6ix + 6i2 + (-1 * -1ix + i * -1ix + x * -1ix) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 Reorder the terms: (-6 + 6i + 6x + -6i + 6ix + 6i2 + (1ix + -1ix2 + -1i2x) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-6 + 6i + 6x + -6i + 6ix + 6i2 + (1ix + -1ix2 + -1i2x) + -7x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-6 + 6i + 6x + -6i + 6ix + 6i2 + 1ix + -1ix2 + -1i2x + (-1 * -7x + i * -7x + x * -7x) + x2(-1 + i + x)) = 0 Reorder the terms: (-6 + 6i + 6x + -6i + 6ix + 6i2 + 1ix + -1ix2 + -1i2x + (-7ix + 7x + -7x2) + x2(-1 + i + x)) = 0 (-6 + 6i + 6x + -6i + 6ix + 6i2 + 1ix + -1ix2 + -1i2x + (-7ix + 7x + -7x2) + x2(-1 + i + x)) = 0 (-6 + 6i + 6x + -6i + 6ix + 6i2 + 1ix + -1ix2 + -1i2x + -7ix + 7x + -7x2 + (-1 * x2 + i * x2 + x * x2)) = 0 Reorder the terms: (-6 + 6i + 6x + -6i + 6ix + 6i2 + 1ix + -1ix2 + -1i2x + -7ix + 7x + -7x2 + (ix2 + -1x2 + x3)) = 0 (-6 + 6i + 6x + -6i + 6ix + 6i2 + 1ix + -1ix2 + -1i2x + -7ix + 7x + -7x2 + (ix2 + -1x2 + x3)) = 0 Reorder the terms: (-6 + 6i + -6i + 6ix + 1ix + -7ix + -1ix2 + ix2 + 6i2 + -1i2x + 6x + 7x + -7x2 + -1x2 + x3) = 0 Combine like terms: 6i + -6i = 0 (-6 + 0 + 6ix + 1ix + -7ix + -1ix2 + ix2 + 6i2 + -1i2x + 6x + 7x + -7x2 + -1x2 + x3) = 0 (-6 + 6ix + 1ix + -7ix + -1ix2 + ix2 + 6i2 + -1i2x + 6x + 7x + -7x2 + -1x2 + x3) = 0 Combine like terms: 6ix + 1ix = 7ix (-6 + 7ix + -7ix + -1ix2 + ix2 + 6i2 + -1i2x + 6x + 7x + -7x2 + -1x2 + x3) = 0 Combine like terms: 7ix + -7ix = 0 (-6 + 0 + -1ix2 + ix2 + 6i2 + -1i2x + 6x + 7x + -7x2 + -1x2 + x3) = 0 (-6 + -1ix2 + ix2 + 6i2 + -1i2x + 6x + 7x + -7x2 + -1x2 + x3) = 0 Combine like terms: -1ix2 + ix2 = 0 (-6 + 0 + 6i2 + -1i2x + 6x + 7x + -7x2 + -1x2 + x3) = 0 (-6 + 6i2 + -1i2x + 6x + 7x + -7x2 + -1x2 + x3) = 0 Combine like terms: 6x + 7x = 13x (-6 + 6i2 + -1i2x + 13x + -7x2 + -1x2 + x3) = 0 Combine like terms: -7x2 + -1x2 = -8x2 (-6 + 6i2 + -1i2x + 13x + -8x2 + x3) = 0 Solving -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6i2 + -1i2x + 13x + -8x2 + 6 + x3 = 0 + 6 Reorder the terms: -6 + 6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6i2 + -1i2x + 13x + -8x2 + x3 = 0 + 6 6i2 + -1i2x + 13x + -8x2 + x3 = 0 + 6 Combine like terms: 0 + 6 = 6 6i2 + -1i2x + 13x + -8x2 + x3 = 6 Add '-13x' to each side of the equation. 6i2 + -1i2x + 13x + -8x2 + -13x + x3 = 6 + -13x Reorder the terms: 6i2 + -1i2x + 13x + -13x + -8x2 + x3 = 6 + -13x Combine like terms: 13x + -13x = 0 6i2 + -1i2x + 0 + -8x2 + x3 = 6 + -13x 6i2 + -1i2x + -8x2 + x3 = 6 + -13x Add '8x2' to each side of the equation. 6i2 + -1i2x + -8x2 + 8x2 + x3 = 6 + -13x + 8x2 Combine like terms: -8x2 + 8x2 = 0 6i2 + -1i2x + 0 + x3 = 6 + -13x + 8x2 6i2 + -1i2x + x3 = 6 + -13x + 8x2 Add '-1x3' to each side of the equation. 6i2 + -1i2x + x3 + -1x3 = 6 + -13x + 8x2 + -1x3 Combine like terms: x3 + -1x3 = 0 6i2 + -1i2x + 0 = 6 + -13x + 8x2 + -1x3 6i2 + -1i2x = 6 + -13x + 8x2 + -1x3 Reorder the terms: -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 6 + -13x + 8x2 + -1x3 + -6 + 13x + -8x2 + x3 Reorder the terms: -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 6 + -6 + -13x + 13x + 8x2 + -8x2 + -1x3 + x3 Combine like terms: 6 + -6 = 0 -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 0 + -13x + 13x + 8x2 + -8x2 + -1x3 + x3 -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = -13x + 13x + 8x2 + -8x2 + -1x3 + x3 Combine like terms: -13x + 13x = 0 -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 0 + 8x2 + -8x2 + -1x3 + x3 -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 8x2 + -8x2 + -1x3 + x3 Combine like terms: 8x2 + -8x2 = 0 -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 0 + -1x3 + x3 -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -6 + 6i2 + -1i2x + 13x + -8x2 + x3 = 0 The solution to this equation could not be determined.
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