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Simplifying (x + -3)(x + 2)(x + -1 + -3i)(x + -1 + 3i) = 60 Reorder the terms: (-3 + x)(x + 2)(x + -1 + -3i)(x + -1 + 3i) = 60 Reorder the terms: (-3 + x)(2 + x)(x + -1 + -3i)(x + -1 + 3i) = 60 Reorder the terms: (-3 + x)(2 + x)(-1 + -3i + x)(x + -1 + 3i) = 60 Reorder the terms: (-3 + x)(2 + x)(-1 + -3i + x)(-1 + 3i + x) = 60 Multiply (-3 + x) * (2 + x) (-3(2 + x) + x(2 + x))(-1 + -3i + x)(-1 + 3i + x) = 60 ((2 * -3 + x * -3) + x(2 + x))(-1 + -3i + x)(-1 + 3i + x) = 60 ((-6 + -3x) + x(2 + x))(-1 + -3i + x)(-1 + 3i + x) = 60 (-6 + -3x + (2 * x + x * x))(-1 + -3i + x)(-1 + 3i + x) = 60 (-6 + -3x + (2x + x2))(-1 + -3i + x)(-1 + 3i + x) = 60 Combine like terms: -3x + 2x = -1x (-6 + -1x + x2)(-1 + -3i + x)(-1 + 3i + x) = 60 Multiply (-6 + -1x + x2) * (-1 + -3i + x) (-6(-1 + -3i + x) + -1x * (-1 + -3i + x) + x2(-1 + -3i + x))(-1 + 3i + x) = 60 ((-1 * -6 + -3i * -6 + x * -6) + -1x * (-1 + -3i + x) + x2(-1 + -3i + x))(-1 + 3i + x) = 60 ((6 + 18i + -6x) + -1x * (-1 + -3i + x) + x2(-1 + -3i + x))(-1 + 3i + x) = 60 (6 + 18i + -6x + (-1 * -1x + -3i * -1x + x * -1x) + x2(-1 + -3i + x))(-1 + 3i + x) = 60 Reorder the terms: (6 + 18i + -6x + (3ix + 1x + -1x2) + x2(-1 + -3i + x))(-1 + 3i + x) = 60 (6 + 18i + -6x + (3ix + 1x + -1x2) + x2(-1 + -3i + x))(-1 + 3i + x) = 60 (6 + 18i + -6x + 3ix + 1x + -1x2 + (-1 * x2 + -3i * x2 + x * x2))(-1 + 3i + x) = 60 Reorder the terms: (6 + 18i + -6x + 3ix + 1x + -1x2 + (-3ix2 + -1x2 + x3))(-1 + 3i + x) = 60 (6 + 18i + -6x + 3ix + 1x + -1x2 + (-3ix2 + -1x2 + x3))(-1 + 3i + x) = 60 Reorder the terms: (6 + 18i + 3ix + -3ix2 + -6x + 1x + -1x2 + -1x2 + x3)(-1 + 3i + x) = 60 Combine like terms: -6x + 1x = -5x (6 + 18i + 3ix + -3ix2 + -5x + -1x2 + -1x2 + x3)(-1 + 3i + x) = 60 Combine like terms: -1x2 + -1x2 = -2x2 (6 + 18i + 3ix + -3ix2 + -5x + -2x2 + x3)(-1 + 3i + x) = 60 Multiply (6 + 18i + 3ix + -3ix2 + -5x + -2x2 + x3) * (-1 + 3i + x) (6(-1 + 3i + x) + 18i * (-1 + 3i + x) + 3ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 ((-1 * 6 + 3i * 6 + x * 6) + 18i * (-1 + 3i + x) + 3ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 ((-6 + 18i + 6x) + 18i * (-1 + 3i + x) + 3ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + (-1 * 18i + 3i * 18i + x * 18i) + 3ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 Reorder the terms: (-6 + 18i + 6x + (-18i + 18ix + 54i2) + 3ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + (-18i + 18ix + 54i2) + 3ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + (-1 * 3ix + 3i * 3ix + x * 3ix) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 Reorder the terms: (-6 + 18i + 6x + -18i + 18ix + 54i2 + (-3ix + 3ix2 + 9i2x) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + (-3ix + 3ix2 + 9i2x) + -3ix2 * (-1 + 3i + x) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + (-1 * -3ix2 + 3i * -3ix2 + x * -3ix2) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 Reorder the terms: (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + (3ix2 + -3ix3 + -9i2x2) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + (3ix2 + -3ix3 + -9i2x2) + -5x * (-1 + 3i + x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + (-1 * -5x + 3i * -5x + x * -5x) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 Reorder the terms: (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + (-15ix + 5x + -5x2) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + (-15ix + 5x + -5x2) + -2x2 * (-1 + 3i + x) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + -15ix + 5x + -5x2 + (-1 * -2x2 + 3i * -2x2 + x * -2x2) + x3(-1 + 3i + x)) = 60 Reorder the terms: (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + -15ix + 5x + -5x2 + (-6ix2 + 2x2 + -2x3) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + -15ix + 5x + -5x2 + (-6ix2 + 2x2 + -2x3) + x3(-1 + 3i + x)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + -15ix + 5x + -5x2 + -6ix2 + 2x2 + -2x3 + (-1 * x3 + 3i * x3 + x * x3)) = 60 Reorder the terms: (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + -15ix + 5x + -5x2 + -6ix2 + 2x2 + -2x3 + (3ix3 + -1x3 + x4)) = 60 (-6 + 18i + 6x + -18i + 18ix + 54i2 + -3ix + 3ix2 + 9i2x + 3ix2 + -3ix3 + -9i2x2 + -15ix + 5x + -5x2 + -6ix2 + 2x2 + -2x3 + (3ix3 + -1x3 + x4)) = 60 Reorder the terms: (-6 + 18i + -18i + 18ix + -3ix + -15ix + 3ix2 + 3ix2 + -6ix2 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: 18i + -18i = 0 (-6 + 0 + 18ix + -3ix + -15ix + 3ix2 + 3ix2 + -6ix2 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 (-6 + 18ix + -3ix + -15ix + 3ix2 + 3ix2 + -6ix2 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: 18ix + -3ix = 15ix (-6 + 15ix + -15ix + 3ix2 + 3ix2 + -6ix2 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: 15ix + -15ix = 0 (-6 + 0 + 3ix2 + 3ix2 + -6ix2 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 (-6 + 3ix2 + 3ix2 + -6ix2 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: 3ix2 + 3ix2 = 6ix2 (-6 + 6ix2 + -6ix2 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: 6ix2 + -6ix2 = 0 (-6 + 0 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 (-6 + -3ix3 + 3ix3 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: -3ix3 + 3ix3 = 0 (-6 + 0 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 (-6 + 54i2 + 9i2x + -9i2x2 + 6x + 5x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: 6x + 5x = 11x (-6 + 54i2 + 9i2x + -9i2x2 + 11x + -5x2 + 2x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: -5x2 + 2x2 = -3x2 (-6 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -2x3 + -1x3 + x4) = 60 Combine like terms: -2x3 + -1x3 = -3x3 (-6 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4) = 60 Solving -6 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 60 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 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + 6 + x4 = 60 + 6 Reorder the terms: -6 + 6 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 60 + 6 Combine like terms: -6 + 6 = 0 0 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 60 + 6 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 60 + 6 Combine like terms: 60 + 6 = 66 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 66 Add '-11x' to each side of the equation. 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + -11x + x4 = 66 + -11x Reorder the terms: 54i2 + 9i2x + -9i2x2 + 11x + -11x + -3x2 + -3x3 + x4 = 66 + -11x Combine like terms: 11x + -11x = 0 54i2 + 9i2x + -9i2x2 + 0 + -3x2 + -3x3 + x4 = 66 + -11x 54i2 + 9i2x + -9i2x2 + -3x2 + -3x3 + x4 = 66 + -11x Add '3x2' to each side of the equation. 54i2 + 9i2x + -9i2x2 + -3x2 + -3x3 + 3x2 + x4 = 66 + -11x + 3x2 Reorder the terms: 54i2 + 9i2x + -9i2x2 + -3x2 + 3x2 + -3x3 + x4 = 66 + -11x + 3x2 Combine like terms: -3x2 + 3x2 = 0 54i2 + 9i2x + -9i2x2 + 0 + -3x3 + x4 = 66 + -11x + 3x2 54i2 + 9i2x + -9i2x2 + -3x3 + x4 = 66 + -11x + 3x2 Add '3x3' to each side of the equation. 54i2 + 9i2x + -9i2x2 + -3x3 + 3x3 + x4 = 66 + -11x + 3x2 + 3x3 Combine like terms: -3x3 + 3x3 = 0 54i2 + 9i2x + -9i2x2 + 0 + x4 = 66 + -11x + 3x2 + 3x3 54i2 + 9i2x + -9i2x2 + x4 = 66 + -11x + 3x2 + 3x3 Add '-1x4' to each side of the equation. 54i2 + 9i2x + -9i2x2 + x4 + -1x4 = 66 + -11x + 3x2 + 3x3 + -1x4 Combine like terms: x4 + -1x4 = 0 54i2 + 9i2x + -9i2x2 + 0 = 66 + -11x + 3x2 + 3x3 + -1x4 54i2 + 9i2x + -9i2x2 = 66 + -11x + 3x2 + 3x3 + -1x4 Reorder the terms: -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 66 + -11x + 3x2 + 3x3 + -1x4 + -66 + 11x + -3x2 + -3x3 + x4 Reorder the terms: -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 66 + -66 + -11x + 11x + 3x2 + -3x2 + 3x3 + -3x3 + -1x4 + x4 Combine like terms: 66 + -66 = 0 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 0 + -11x + 11x + 3x2 + -3x2 + 3x3 + -3x3 + -1x4 + x4 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = -11x + 11x + 3x2 + -3x2 + 3x3 + -3x3 + -1x4 + x4 Combine like terms: -11x + 11x = 0 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 0 + 3x2 + -3x2 + 3x3 + -3x3 + -1x4 + x4 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 3x2 + -3x2 + 3x3 + -3x3 + -1x4 + x4 Combine like terms: 3x2 + -3x2 = 0 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 0 + 3x3 + -3x3 + -1x4 + x4 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 3x3 + -3x3 + -1x4 + x4 Combine like terms: 3x3 + -3x3 = 0 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 0 + -1x4 + x4 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -66 + 54i2 + 9i2x + -9i2x2 + 11x + -3x2 + -3x3 + x4 = 0 The solution to this equation could not be determined.
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