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Simplifying (X + -1(-4 + 3i))(x + -1(-4 + -3i)) = 0 (X + (-4 * -1 + 3i * -1))(x + -1(-4 + -3i)) = 0 (X + (4 + -3i))(x + -1(-4 + -3i)) = 0 Reorder the terms: (4 + X + -3i)(x + -1(-4 + -3i)) = 0 (4 + X + -3i)(x + (-4 * -1 + -3i * -1)) = 0 (4 + X + -3i)(x + (4 + 3i)) = 0 Reorder the terms: (4 + X + -3i)(4 + 3i + x) = 0 Multiply (4 + X + -3i) * (4 + 3i + x) (4(4 + 3i + x) + X(4 + 3i + x) + -3i * (4 + 3i + x)) = 0 ((4 * 4 + 3i * 4 + x * 4) + X(4 + 3i + x) + -3i * (4 + 3i + x)) = 0 ((16 + 12i + 4x) + X(4 + 3i + x) + -3i * (4 + 3i + x)) = 0 (16 + 12i + 4x + (4 * X + 3i * X + x * X) + -3i * (4 + 3i + x)) = 0 (16 + 12i + 4x + (4X + 3iX + xX) + -3i * (4 + 3i + x)) = 0 (16 + 12i + 4x + 4X + 3iX + xX + (4 * -3i + 3i * -3i + x * -3i)) = 0 Reorder the terms: (16 + 12i + 4x + 4X + 3iX + xX + (-12i + -3ix + -9i2)) = 0 (16 + 12i + 4x + 4X + 3iX + xX + (-12i + -3ix + -9i2)) = 0 Reorder the terms: (16 + 4X + 12i + -12i + 3iX + -3ix + -9i2 + 4x + xX) = 0 Combine like terms: 12i + -12i = 0 (16 + 4X + 0 + 3iX + -3ix + -9i2 + 4x + xX) = 0 (16 + 4X + 3iX + -3ix + -9i2 + 4x + xX) = 0 Solving 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + 4X + 3iX + -3ix + -9i2 + 4x + -16 + xX = 0 + -16 Reorder the terms: 16 + -16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 0 + -16 4X + 3iX + -3ix + -9i2 + 4x + xX = 0 + -16 Combine like terms: 0 + -16 = -16 4X + 3iX + -3ix + -9i2 + 4x + xX = -16 Add '3ix' to each side of the equation. 4X + 3iX + -3ix + -9i2 + 4x + 3ix + xX = -16 + 3ix Reorder the terms: 4X + 3iX + -3ix + 3ix + -9i2 + 4x + xX = -16 + 3ix Combine like terms: -3ix + 3ix = 0 4X + 3iX + 0 + -9i2 + 4x + xX = -16 + 3ix 4X + 3iX + -9i2 + 4x + xX = -16 + 3ix Add '9i2' to each side of the equation. 4X + 3iX + -9i2 + 4x + 9i2 + xX = -16 + 3ix + 9i2 Reorder the terms: 4X + 3iX + -9i2 + 9i2 + 4x + xX = -16 + 3ix + 9i2 Combine like terms: -9i2 + 9i2 = 0 4X + 3iX + 0 + 4x + xX = -16 + 3ix + 9i2 4X + 3iX + 4x + xX = -16 + 3ix + 9i2 Add '-4x' to each side of the equation. 4X + 3iX + 4x + -4x + xX = -16 + 3ix + 9i2 + -4x Combine like terms: 4x + -4x = 0 4X + 3iX + 0 + xX = -16 + 3ix + 9i2 + -4x 4X + 3iX + xX = -16 + 3ix + 9i2 + -4x Reorder the terms: 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = -16 + 3ix + 9i2 + -4x + 16 + -3ix + -9i2 + 4x Reorder the terms: 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = -16 + 16 + 3ix + -3ix + 9i2 + -9i2 + -4x + 4x Combine like terms: -16 + 16 = 0 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 0 + 3ix + -3ix + 9i2 + -9i2 + -4x + 4x 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 3ix + -3ix + 9i2 + -9i2 + -4x + 4x Combine like terms: 3ix + -3ix = 0 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 0 + 9i2 + -9i2 + -4x + 4x 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 9i2 + -9i2 + -4x + 4x Combine like terms: 9i2 + -9i2 = 0 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 0 + -4x + 4x 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = -4x + 4x Combine like terms: -4x + 4x = 0 16 + 4X + 3iX + -3ix + -9i2 + 4x + xX = 0 The solution to this equation could not be determined.
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