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Simplifying (x + -1(1 + i))(x + -1(1 + -1i))(x + -3) = 0 (x + (1 * -1 + i * -1))(x + -1(1 + -1i))(x + -3) = 0 (x + (-1 + -1i))(x + -1(1 + -1i))(x + -3) = 0 Reorder the terms: (-1 + -1i + x)(x + -1(1 + -1i))(x + -3) = 0 (-1 + -1i + x)(x + (1 * -1 + -1i * -1))(x + -3) = 0 (-1 + -1i + x)(x + (-1 + 1i))(x + -3) = 0 Reorder the terms: (-1 + -1i + x)(-1 + 1i + x)(x + -3) = 0 Reorder the terms: (-1 + -1i + x)(-1 + 1i + x)(-3 + x) = 0 Multiply (-1 + -1i + x) * (-1 + 1i + x) (-1(-1 + 1i + x) + -1i * (-1 + 1i + x) + x(-1 + 1i + x))(-3 + x) = 0 ((-1 * -1 + 1i * -1 + x * -1) + -1i * (-1 + 1i + x) + x(-1 + 1i + x))(-3 + x) = 0 ((1 + -1i + -1x) + -1i * (-1 + 1i + x) + x(-1 + 1i + x))(-3 + x) = 0 (1 + -1i + -1x + (-1 * -1i + 1i * -1i + x * -1i) + x(-1 + 1i + x))(-3 + x) = 0 Reorder the terms: (1 + -1i + -1x + (1i + -1ix + -1i2) + x(-1 + 1i + x))(-3 + x) = 0 (1 + -1i + -1x + (1i + -1ix + -1i2) + x(-1 + 1i + x))(-3 + x) = 0 (1 + -1i + -1x + 1i + -1ix + -1i2 + (-1 * x + 1i * x + x * x))(-3 + x) = 0 Reorder the terms: (1 + -1i + -1x + 1i + -1ix + -1i2 + (1ix + -1x + x2))(-3 + x) = 0 (1 + -1i + -1x + 1i + -1ix + -1i2 + (1ix + -1x + x2))(-3 + x) = 0 Reorder the terms: (1 + -1i + 1i + -1ix + 1ix + -1i2 + -1x + -1x + x2)(-3 + x) = 0 Combine like terms: -1i + 1i = 0 (1 + 0 + -1ix + 1ix + -1i2 + -1x + -1x + x2)(-3 + x) = 0 (1 + -1ix + 1ix + -1i2 + -1x + -1x + x2)(-3 + x) = 0 Combine like terms: -1ix + 1ix = 0 (1 + 0 + -1i2 + -1x + -1x + x2)(-3 + x) = 0 (1 + -1i2 + -1x + -1x + x2)(-3 + x) = 0 Combine like terms: -1x + -1x = -2x (1 + -1i2 + -2x + x2)(-3 + x) = 0 Multiply (1 + -1i2 + -2x + x2) * (-3 + x) (1(-3 + x) + -1i2 * (-3 + x) + -2x * (-3 + x) + x2(-3 + x)) = 0 ((-3 * 1 + x * 1) + -1i2 * (-3 + x) + -2x * (-3 + x) + x2(-3 + x)) = 0 ((-3 + 1x) + -1i2 * (-3 + x) + -2x * (-3 + x) + x2(-3 + x)) = 0 (-3 + 1x + (-3 * -1i2 + x * -1i2) + -2x * (-3 + x) + x2(-3 + x)) = 0 (-3 + 1x + (3i2 + -1i2x) + -2x * (-3 + x) + x2(-3 + x)) = 0 (-3 + 1x + 3i2 + -1i2x + (-3 * -2x + x * -2x) + x2(-3 + x)) = 0 (-3 + 1x + 3i2 + -1i2x + (6x + -2x2) + x2(-3 + x)) = 0 (-3 + 1x + 3i2 + -1i2x + 6x + -2x2 + (-3 * x2 + x * x2)) = 0 (-3 + 1x + 3i2 + -1i2x + 6x + -2x2 + (-3x2 + x3)) = 0 Reorder the terms: (-3 + 3i2 + -1i2x + 1x + 6x + -2x2 + -3x2 + x3) = 0 Combine like terms: 1x + 6x = 7x (-3 + 3i2 + -1i2x + 7x + -2x2 + -3x2 + x3) = 0 Combine like terms: -2x2 + -3x2 = -5x2 (-3 + 3i2 + -1i2x + 7x + -5x2 + x3) = 0 Solving -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3i2 + -1i2x + 7x + -5x2 + 3 + x3 = 0 + 3 Reorder the terms: -3 + 3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3i2 + -1i2x + 7x + -5x2 + x3 = 0 + 3 3i2 + -1i2x + 7x + -5x2 + x3 = 0 + 3 Combine like terms: 0 + 3 = 3 3i2 + -1i2x + 7x + -5x2 + x3 = 3 Add '-7x' to each side of the equation. 3i2 + -1i2x + 7x + -5x2 + -7x + x3 = 3 + -7x Reorder the terms: 3i2 + -1i2x + 7x + -7x + -5x2 + x3 = 3 + -7x Combine like terms: 7x + -7x = 0 3i2 + -1i2x + 0 + -5x2 + x3 = 3 + -7x 3i2 + -1i2x + -5x2 + x3 = 3 + -7x Add '5x2' to each side of the equation. 3i2 + -1i2x + -5x2 + 5x2 + x3 = 3 + -7x + 5x2 Combine like terms: -5x2 + 5x2 = 0 3i2 + -1i2x + 0 + x3 = 3 + -7x + 5x2 3i2 + -1i2x + x3 = 3 + -7x + 5x2 Add '-1x3' to each side of the equation. 3i2 + -1i2x + x3 + -1x3 = 3 + -7x + 5x2 + -1x3 Combine like terms: x3 + -1x3 = 0 3i2 + -1i2x + 0 = 3 + -7x + 5x2 + -1x3 3i2 + -1i2x = 3 + -7x + 5x2 + -1x3 Reorder the terms: -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 3 + -7x + 5x2 + -1x3 + -3 + 7x + -5x2 + x3 Reorder the terms: -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 3 + -3 + -7x + 7x + 5x2 + -5x2 + -1x3 + x3 Combine like terms: 3 + -3 = 0 -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 0 + -7x + 7x + 5x2 + -5x2 + -1x3 + x3 -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = -7x + 7x + 5x2 + -5x2 + -1x3 + x3 Combine like terms: -7x + 7x = 0 -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 0 + 5x2 + -5x2 + -1x3 + x3 -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3 Combine like terms: 5x2 + -5x2 = 0 -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 0 + -1x3 + x3 -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -3 + 3i2 + -1i2x + 7x + -5x2 + x3 = 0 The solution to this equation could not be determined.
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