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Simplifying (x + (2 + i))(x + -1(2 + -1i))(x + 7)(x + -5) = 0 Remove parenthesis around (2 + i) (x + 2 + i)(x + -1(2 + -1i))(x + 7)(x + -5) = 0 Reorder the terms: (2 + i + x)(x + -1(2 + -1i))(x + 7)(x + -5) = 0 (2 + i + x)(x + (2 * -1 + -1i * -1))(x + 7)(x + -5) = 0 (2 + i + x)(x + (-2 + 1i))(x + 7)(x + -5) = 0 Reorder the terms: (2 + i + x)(-2 + 1i + x)(x + 7)(x + -5) = 0 Reorder the terms: (2 + i + x)(-2 + 1i + x)(7 + x)(x + -5) = 0 Reorder the terms: (2 + i + x)(-2 + 1i + x)(7 + x)(-5 + x) = 0 Multiply (2 + i + x) * (-2 + 1i + x) (2(-2 + 1i + x) + i(-2 + 1i + x) + x(-2 + 1i + x))(7 + x)(-5 + x) = 0 ((-2 * 2 + 1i * 2 + x * 2) + i(-2 + 1i + x) + x(-2 + 1i + x))(7 + x)(-5 + x) = 0 ((-4 + 2i + 2x) + i(-2 + 1i + x) + x(-2 + 1i + x))(7 + x)(-5 + x) = 0 (-4 + 2i + 2x + (-2 * i + 1i * i + x * i) + x(-2 + 1i + x))(7 + x)(-5 + x) = 0 Reorder the terms: (-4 + 2i + 2x + (-2i + ix + 1i2) + x(-2 + 1i + x))(7 + x)(-5 + x) = 0 (-4 + 2i + 2x + (-2i + ix + 1i2) + x(-2 + 1i + x))(7 + x)(-5 + x) = 0 (-4 + 2i + 2x + -2i + ix + 1i2 + (-2 * x + 1i * x + x * x))(7 + x)(-5 + x) = 0 Reorder the terms: (-4 + 2i + 2x + -2i + ix + 1i2 + (1ix + -2x + x2))(7 + x)(-5 + x) = 0 (-4 + 2i + 2x + -2i + ix + 1i2 + (1ix + -2x + x2))(7 + x)(-5 + x) = 0 Reorder the terms: (-4 + 2i + -2i + ix + 1ix + 1i2 + 2x + -2x + x2)(7 + x)(-5 + x) = 0 Combine like terms: 2i + -2i = 0 (-4 + 0 + ix + 1ix + 1i2 + 2x + -2x + x2)(7 + x)(-5 + x) = 0 (-4 + ix + 1ix + 1i2 + 2x + -2x + x2)(7 + x)(-5 + x) = 0 Combine like terms: ix + 1ix = 2ix (-4 + 2ix + 1i2 + 2x + -2x + x2)(7 + x)(-5 + x) = 0 Combine like terms: 2x + -2x = 0 (-4 + 2ix + 1i2 + 0 + x2)(7 + x)(-5 + x) = 0 (-4 + 2ix + 1i2 + x2)(7 + x)(-5 + x) = 0 Multiply (-4 + 2ix + 1i2 + x2) * (7 + x) (-4(7 + x) + 2ix * (7 + x) + 1i2 * (7 + x) + x2(7 + x))(-5 + x) = 0 ((7 * -4 + x * -4) + 2ix * (7 + x) + 1i2 * (7 + x) + x2(7 + x))(-5 + x) = 0 ((-28 + -4x) + 2ix * (7 + x) + 1i2 * (7 + x) + x2(7 + x))(-5 + x) = 0 (-28 + -4x + (7 * 2ix + x * 2ix) + 1i2 * (7 + x) + x2(7 + x))(-5 + x) = 0 (-28 + -4x + (14ix + 2ix2) + 1i2 * (7 + x) + x2(7 + x))(-5 + x) = 0 (-28 + -4x + 14ix + 2ix2 + (7 * 1i2 + x * 1i2) + x2(7 + x))(-5 + x) = 0 (-28 + -4x + 14ix + 2ix2 + (7i2 + 1i2x) + x2(7 + x))(-5 + x) = 0 (-28 + -4x + 14ix + 2ix2 + 7i2 + 1i2x + (7 * x2 + x * x2))(-5 + x) = 0 (-28 + -4x + 14ix + 2ix2 + 7i2 + 1i2x + (7x2 + x3))(-5 + x) = 0 Reorder the terms: (-28 + 14ix + 2ix2 + 7i2 + 1i2x + -4x + 7x2 + x3)(-5 + x) = 0 (-28 + 14ix + 2ix2 + 7i2 + 1i2x + -4x + 7x2 + x3)(-5 + x) = 0 Multiply (-28 + 14ix + 2ix2 + 7i2 + 1i2x + -4x + 7x2 + x3) * (-5 + x) (-28(-5 + x) + 14ix * (-5 + x) + 2ix2 * (-5 + x) + 7i2 * (-5 + x) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 ((-5 * -28 + x * -28) + 14ix * (-5 + x) + 2ix2 * (-5 + x) + 7i2 * (-5 + x) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 ((140 + -28x) + 14ix * (-5 + x) + 2ix2 * (-5 + x) + 7i2 * (-5 + x) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + (-5 * 14ix + x * 14ix) + 2ix2 * (-5 + x) + 7i2 * (-5 + x) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + (-70ix + 14ix2) + 2ix2 * (-5 + x) + 7i2 * (-5 + x) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + (-5 * 2ix2 + x * 2ix2) + 7i2 * (-5 + x) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + (-10ix2 + 2ix3) + 7i2 * (-5 + x) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + (-5 * 7i2 + x * 7i2) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + (-35i2 + 7i2x) + 1i2x * (-5 + x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + (-5 * 1i2x + x * 1i2x) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + (-5i2x + 1i2x2) + -4x * (-5 + x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + -5i2x + 1i2x2 + (-5 * -4x + x * -4x) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + -5i2x + 1i2x2 + (20x + -4x2) + 7x2 * (-5 + x) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + -5i2x + 1i2x2 + 20x + -4x2 + (-5 * 7x2 + x * 7x2) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + -5i2x + 1i2x2 + 20x + -4x2 + (-35x2 + 7x3) + x3(-5 + x)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + -5i2x + 1i2x2 + 20x + -4x2 + -35x2 + 7x3 + (-5 * x3 + x * x3)) = 0 (140 + -28x + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + -5i2x + 1i2x2 + 20x + -4x2 + -35x2 + 7x3 + (-5x3 + x4)) = 0 Reorder the terms: (140 + -70ix + 14ix2 + -10ix2 + 2ix3 + -35i2 + 7i2x + -5i2x + 1i2x2 + -28x + 20x + -4x2 + -35x2 + 7x3 + -5x3 + x4) = 0 Combine like terms: 14ix2 + -10ix2 = 4ix2 (140 + -70ix + 4ix2 + 2ix3 + -35i2 + 7i2x + -5i2x + 1i2x2 + -28x + 20x + -4x2 + -35x2 + 7x3 + -5x3 + x4) = 0 Combine like terms: 7i2x + -5i2x = 2i2x (140 + -70ix + 4ix2 + 2ix3 + -35i2 + 2i2x + 1i2x2 + -28x + 20x + -4x2 + -35x2 + 7x3 + -5x3 + x4) = 0 Combine like terms: -28x + 20x = -8x (140 + -70ix + 4ix2 + 2ix3 + -35i2 + 2i2x + 1i2x2 + -8x + -4x2 + -35x2 + 7x3 + -5x3 + x4) = 0 Combine like terms: -4x2 + -35x2 = -39x2 (140 + -70ix + 4ix2 + 2ix3 + -35i2 + 2i2x + 1i2x2 + -8x + -39x2 + 7x3 + -5x3 + x4) = 0 Combine like terms: 7x3 + -5x3 = 2x3 (140 + -70ix + 4ix2 + 2ix3 + -35i2 + 2i2x + 1i2x2 + -8x + -39x2 + 2x3 + x4) = 0 Solving 140 + -70ix + 4ix2 + 2ix3 + -35i2 + 2i2x + 1i2x2 + -8x + -39x2 + 2x3 + x4 = 0 Solving for variable 'i'. The solution to this equation could not be determined.
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