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Simplifying (x + -1(3 + 2i))(x + -1(3 + -2i))(x + -4)(x + -4) = 0 (x + (3 * -1 + 2i * -1))(x + -1(3 + -2i))(x + -4)(x + -4) = 0 (x + (-3 + -2i))(x + -1(3 + -2i))(x + -4)(x + -4) = 0 Reorder the terms: (-3 + -2i + x)(x + -1(3 + -2i))(x + -4)(x + -4) = 0 (-3 + -2i + x)(x + (3 * -1 + -2i * -1))(x + -4)(x + -4) = 0 (-3 + -2i + x)(x + (-3 + 2i))(x + -4)(x + -4) = 0 Reorder the terms: (-3 + -2i + x)(-3 + 2i + x)(x + -4)(x + -4) = 0 Reorder the terms: (-3 + -2i + x)(-3 + 2i + x)(-4 + x)(x + -4) = 0 Reorder the terms: (-3 + -2i + x)(-3 + 2i + x)(-4 + x)(-4 + x) = 0 Multiply (-3 + -2i + x) * (-3 + 2i + x) (-3(-3 + 2i + x) + -2i * (-3 + 2i + x) + x(-3 + 2i + x))(-4 + x)(-4 + x) = 0 ((-3 * -3 + 2i * -3 + x * -3) + -2i * (-3 + 2i + x) + x(-3 + 2i + x))(-4 + x)(-4 + x) = 0 ((9 + -6i + -3x) + -2i * (-3 + 2i + x) + x(-3 + 2i + x))(-4 + x)(-4 + x) = 0 (9 + -6i + -3x + (-3 * -2i + 2i * -2i + x * -2i) + x(-3 + 2i + x))(-4 + x)(-4 + x) = 0 Reorder the terms: (9 + -6i + -3x + (6i + -2ix + -4i2) + x(-3 + 2i + x))(-4 + x)(-4 + x) = 0 (9 + -6i + -3x + (6i + -2ix + -4i2) + x(-3 + 2i + x))(-4 + x)(-4 + x) = 0 (9 + -6i + -3x + 6i + -2ix + -4i2 + (-3 * x + 2i * x + x * x))(-4 + x)(-4 + x) = 0 Reorder the terms: (9 + -6i + -3x + 6i + -2ix + -4i2 + (2ix + -3x + x2))(-4 + x)(-4 + x) = 0 (9 + -6i + -3x + 6i + -2ix + -4i2 + (2ix + -3x + x2))(-4 + x)(-4 + x) = 0 Reorder the terms: (9 + -6i + 6i + -2ix + 2ix + -4i2 + -3x + -3x + x2)(-4 + x)(-4 + x) = 0 Combine like terms: -6i + 6i = 0 (9 + 0 + -2ix + 2ix + -4i2 + -3x + -3x + x2)(-4 + x)(-4 + x) = 0 (9 + -2ix + 2ix + -4i2 + -3x + -3x + x2)(-4 + x)(-4 + x) = 0 Combine like terms: -2ix + 2ix = 0 (9 + 0 + -4i2 + -3x + -3x + x2)(-4 + x)(-4 + x) = 0 (9 + -4i2 + -3x + -3x + x2)(-4 + x)(-4 + x) = 0 Combine like terms: -3x + -3x = -6x (9 + -4i2 + -6x + x2)(-4 + x)(-4 + x) = 0 Multiply (9 + -4i2 + -6x + x2) * (-4 + x) (9(-4 + x) + -4i2 * (-4 + x) + -6x * (-4 + x) + x2(-4 + x))(-4 + x) = 0 ((-4 * 9 + x * 9) + -4i2 * (-4 + x) + -6x * (-4 + x) + x2(-4 + x))(-4 + x) = 0 ((-36 + 9x) + -4i2 * (-4 + x) + -6x * (-4 + x) + x2(-4 + x))(-4 + x) = 0 (-36 + 9x + (-4 * -4i2 + x * -4i2) + -6x * (-4 + x) + x2(-4 + x))(-4 + x) = 0 (-36 + 9x + (16i2 + -4i2x) + -6x * (-4 + x) + x2(-4 + x))(-4 + x) = 0 (-36 + 9x + 16i2 + -4i2x + (-4 * -6x + x * -6x) + x2(-4 + x))(-4 + x) = 0 (-36 + 9x + 16i2 + -4i2x + (24x + -6x2) + x2(-4 + x))(-4 + x) = 0 (-36 + 9x + 16i2 + -4i2x + 24x + -6x2 + (-4 * x2 + x * x2))(-4 + x) = 0 (-36 + 9x + 16i2 + -4i2x + 24x + -6x2 + (-4x2 + x3))(-4 + x) = 0 Reorder the terms: (-36 + 16i2 + -4i2x + 9x + 24x + -6x2 + -4x2 + x3)(-4 + x) = 0 Combine like terms: 9x + 24x = 33x (-36 + 16i2 + -4i2x + 33x + -6x2 + -4x2 + x3)(-4 + x) = 0 Combine like terms: -6x2 + -4x2 = -10x2 (-36 + 16i2 + -4i2x + 33x + -10x2 + x3)(-4 + x) = 0 Multiply (-36 + 16i2 + -4i2x + 33x + -10x2 + x3) * (-4 + x) (-36(-4 + x) + 16i2 * (-4 + x) + -4i2x * (-4 + x) + 33x * (-4 + x) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 ((-4 * -36 + x * -36) + 16i2 * (-4 + x) + -4i2x * (-4 + x) + 33x * (-4 + x) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 ((144 + -36x) + 16i2 * (-4 + x) + -4i2x * (-4 + x) + 33x * (-4 + x) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 (144 + -36x + (-4 * 16i2 + x * 16i2) + -4i2x * (-4 + x) + 33x * (-4 + x) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 (144 + -36x + (-64i2 + 16i2x) + -4i2x * (-4 + x) + 33x * (-4 + x) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 (144 + -36x + -64i2 + 16i2x + (-4 * -4i2x + x * -4i2x) + 33x * (-4 + x) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 (144 + -36x + -64i2 + 16i2x + (16i2x + -4i2x2) + 33x * (-4 + x) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 (144 + -36x + -64i2 + 16i2x + 16i2x + -4i2x2 + (-4 * 33x + x * 33x) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 (144 + -36x + -64i2 + 16i2x + 16i2x + -4i2x2 + (-132x + 33x2) + -10x2 * (-4 + x) + x3(-4 + x)) = 0 (144 + -36x + -64i2 + 16i2x + 16i2x + -4i2x2 + -132x + 33x2 + (-4 * -10x2 + x * -10x2) + x3(-4 + x)) = 0 (144 + -36x + -64i2 + 16i2x + 16i2x + -4i2x2 + -132x + 33x2 + (40x2 + -10x3) + x3(-4 + x)) = 0 (144 + -36x + -64i2 + 16i2x + 16i2x + -4i2x2 + -132x + 33x2 + 40x2 + -10x3 + (-4 * x3 + x * x3)) = 0 (144 + -36x + -64i2 + 16i2x + 16i2x + -4i2x2 + -132x + 33x2 + 40x2 + -10x3 + (-4x3 + x4)) = 0 Reorder the terms: (144 + -64i2 + 16i2x + 16i2x + -4i2x2 + -36x + -132x + 33x2 + 40x2 + -10x3 + -4x3 + x4) = 0 Combine like terms: 16i2x + 16i2x = 32i2x (144 + -64i2 + 32i2x + -4i2x2 + -36x + -132x + 33x2 + 40x2 + -10x3 + -4x3 + x4) = 0 Combine like terms: -36x + -132x = -168x (144 + -64i2 + 32i2x + -4i2x2 + -168x + 33x2 + 40x2 + -10x3 + -4x3 + x4) = 0 Combine like terms: 33x2 + 40x2 = 73x2 (144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -10x3 + -4x3 + x4) = 0 Combine like terms: -10x3 + -4x3 = -14x3 (144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4) = 0 Solving 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-144' to each side of the equation. 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + -144 + x4 = 0 + -144 Reorder the terms: 144 + -144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -144 -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -144 Combine like terms: 0 + -144 = -144 -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = -144 Add '168x' to each side of the equation. -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + 168x + x4 = -144 + 168x Reorder the terms: -64i2 + 32i2x + -4i2x2 + -168x + 168x + 73x2 + -14x3 + x4 = -144 + 168x Combine like terms: -168x + 168x = 0 -64i2 + 32i2x + -4i2x2 + 0 + 73x2 + -14x3 + x4 = -144 + 168x -64i2 + 32i2x + -4i2x2 + 73x2 + -14x3 + x4 = -144 + 168x Add '-73x2' to each side of the equation. -64i2 + 32i2x + -4i2x2 + 73x2 + -14x3 + -73x2 + x4 = -144 + 168x + -73x2 Reorder the terms: -64i2 + 32i2x + -4i2x2 + 73x2 + -73x2 + -14x3 + x4 = -144 + 168x + -73x2 Combine like terms: 73x2 + -73x2 = 0 -64i2 + 32i2x + -4i2x2 + 0 + -14x3 + x4 = -144 + 168x + -73x2 -64i2 + 32i2x + -4i2x2 + -14x3 + x4 = -144 + 168x + -73x2 Add '14x3' to each side of the equation. -64i2 + 32i2x + -4i2x2 + -14x3 + 14x3 + x4 = -144 + 168x + -73x2 + 14x3 Combine like terms: -14x3 + 14x3 = 0 -64i2 + 32i2x + -4i2x2 + 0 + x4 = -144 + 168x + -73x2 + 14x3 -64i2 + 32i2x + -4i2x2 + x4 = -144 + 168x + -73x2 + 14x3 Add '-1x4' to each side of the equation. -64i2 + 32i2x + -4i2x2 + x4 + -1x4 = -144 + 168x + -73x2 + 14x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -64i2 + 32i2x + -4i2x2 + 0 = -144 + 168x + -73x2 + 14x3 + -1x4 -64i2 + 32i2x + -4i2x2 = -144 + 168x + -73x2 + 14x3 + -1x4 Reorder the terms: 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = -144 + 168x + -73x2 + 14x3 + -1x4 + 144 + -168x + 73x2 + -14x3 + x4 Reorder the terms: 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = -144 + 144 + 168x + -168x + -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 Combine like terms: -144 + 144 = 0 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + 168x + -168x + -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 168x + -168x + -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 Combine like terms: 168x + -168x = 0 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 Combine like terms: -73x2 + 73x2 = 0 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + 14x3 + -14x3 + -1x4 + x4 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 14x3 + -14x3 + -1x4 + x4 Combine like terms: 14x3 + -14x3 = 0 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -1x4 + x4 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 144 + -64i2 + 32i2x + -4i2x2 + -168x + 73x2 + -14x3 + x4 = 0 The solution to this equation could not be determined.
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