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Simplifying (x + -7)(x + 3)(x + -3i)(x + 3i) = 0 Reorder the terms: (-7 + x)(x + 3)(x + -3i)(x + 3i) = 0 Reorder the terms: (-7 + x)(3 + x)(x + -3i)(x + 3i) = 0 Reorder the terms: (-7 + x)(3 + x)(-3i + x)(x + 3i) = 0 Reorder the terms: (-7 + x)(3 + x)(-3i + x)(3i + x) = 0 Multiply (-7 + x) * (3 + x) (-7(3 + x) + x(3 + x))(-3i + x)(3i + x) = 0 ((3 * -7 + x * -7) + x(3 + x))(-3i + x)(3i + x) = 0 ((-21 + -7x) + x(3 + x))(-3i + x)(3i + x) = 0 (-21 + -7x + (3 * x + x * x))(-3i + x)(3i + x) = 0 (-21 + -7x + (3x + x2))(-3i + x)(3i + x) = 0 Combine like terms: -7x + 3x = -4x (-21 + -4x + x2)(-3i + x)(3i + x) = 0 Multiply (-21 + -4x + x2) * (-3i + x) (-21(-3i + x) + -4x * (-3i + x) + x2(-3i + x))(3i + x) = 0 ((-3i * -21 + x * -21) + -4x * (-3i + x) + x2(-3i + x))(3i + x) = 0 ((63i + -21x) + -4x * (-3i + x) + x2(-3i + x))(3i + x) = 0 (63i + -21x + (-3i * -4x + x * -4x) + x2(-3i + x))(3i + x) = 0 (63i + -21x + (12ix + -4x2) + x2(-3i + x))(3i + x) = 0 (63i + -21x + 12ix + -4x2 + (-3i * x2 + x * x2))(3i + x) = 0 (63i + -21x + 12ix + -4x2 + (-3ix2 + x3))(3i + x) = 0 Reorder the terms: (63i + 12ix + -3ix2 + -21x + -4x2 + x3)(3i + x) = 0 (63i + 12ix + -3ix2 + -21x + -4x2 + x3)(3i + x) = 0 Multiply (63i + 12ix + -3ix2 + -21x + -4x2 + x3) * (3i + x) (63i * (3i + x) + 12ix * (3i + x) + -3ix2 * (3i + x) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 ((3i * 63i + x * 63i) + 12ix * (3i + x) + -3ix2 * (3i + x) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: ((63ix + 189i2) + 12ix * (3i + x) + -3ix2 * (3i + x) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 ((63ix + 189i2) + 12ix * (3i + x) + -3ix2 * (3i + x) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 (63ix + 189i2 + (3i * 12ix + x * 12ix) + -3ix2 * (3i + x) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: (63ix + 189i2 + (12ix2 + 36i2x) + -3ix2 * (3i + x) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 (63ix + 189i2 + (12ix2 + 36i2x) + -3ix2 * (3i + x) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 (63ix + 189i2 + 12ix2 + 36i2x + (3i * -3ix2 + x * -3ix2) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: (63ix + 189i2 + 12ix2 + 36i2x + (-3ix3 + -9i2x2) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 (63ix + 189i2 + 12ix2 + 36i2x + (-3ix3 + -9i2x2) + -21x * (3i + x) + -4x2 * (3i + x) + x3(3i + x)) = 0 (63ix + 189i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + (3i * -21x + x * -21x) + -4x2 * (3i + x) + x3(3i + x)) = 0 (63ix + 189i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + (-63ix + -21x2) + -4x2 * (3i + x) + x3(3i + x)) = 0 (63ix + 189i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + -63ix + -21x2 + (3i * -4x2 + x * -4x2) + x3(3i + x)) = 0 (63ix + 189i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + -63ix + -21x2 + (-12ix2 + -4x3) + x3(3i + x)) = 0 (63ix + 189i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + -63ix + -21x2 + -12ix2 + -4x3 + (3i * x3 + x * x3)) = 0 (63ix + 189i2 + 12ix2 + 36i2x + -3ix3 + -9i2x2 + -63ix + -21x2 + -12ix2 + -4x3 + (3ix3 + x4)) = 0 Reorder the terms: (63ix + -63ix + 12ix2 + -12ix2 + -3ix3 + 3ix3 + 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4) = 0 Combine like terms: 63ix + -63ix = 0 (0 + 12ix2 + -12ix2 + -3ix3 + 3ix3 + 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4) = 0 (12ix2 + -12ix2 + -3ix3 + 3ix3 + 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4) = 0 Combine like terms: 12ix2 + -12ix2 = 0 (0 + -3ix3 + 3ix3 + 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4) = 0 (-3ix3 + 3ix3 + 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4) = 0 Combine like terms: -3ix3 + 3ix3 = 0 (0 + 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4) = 0 (189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4) = 0 Solving 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '21x2' to each side of the equation. 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + 21x2 + x4 = 0 + 21x2 Reorder the terms: 189i2 + 36i2x + -9i2x2 + -21x2 + 21x2 + -4x3 + x4 = 0 + 21x2 Combine like terms: -21x2 + 21x2 = 0 189i2 + 36i2x + -9i2x2 + 0 + -4x3 + x4 = 0 + 21x2 189i2 + 36i2x + -9i2x2 + -4x3 + x4 = 0 + 21x2 Remove the zero: 189i2 + 36i2x + -9i2x2 + -4x3 + x4 = 21x2 Add '4x3' to each side of the equation. 189i2 + 36i2x + -9i2x2 + -4x3 + 4x3 + x4 = 21x2 + 4x3 Combine like terms: -4x3 + 4x3 = 0 189i2 + 36i2x + -9i2x2 + 0 + x4 = 21x2 + 4x3 189i2 + 36i2x + -9i2x2 + x4 = 21x2 + 4x3 Add '-1x4' to each side of the equation. 189i2 + 36i2x + -9i2x2 + x4 + -1x4 = 21x2 + 4x3 + -1x4 Combine like terms: x4 + -1x4 = 0 189i2 + 36i2x + -9i2x2 + 0 = 21x2 + 4x3 + -1x4 189i2 + 36i2x + -9i2x2 = 21x2 + 4x3 + -1x4 Reorder the terms: 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4 = 21x2 + -21x2 + 4x3 + -4x3 + -1x4 + x4 Combine like terms: 21x2 + -21x2 = 0 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4 = 0 + 4x3 + -4x3 + -1x4 + x4 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4 = 4x3 + -4x3 + -1x4 + x4 Combine like terms: 4x3 + -4x3 = 0 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4 = 0 + -1x4 + x4 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 189i2 + 36i2x + -9i2x2 + -21x2 + -4x3 + x4 = 0 The solution to this equation could not be determined.
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