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Simplifying (x + 2)(x + 2)(-2 + 3i)(-2 + -3i) = 0 Reorder the terms: (2 + x)(x + 2)(-2 + 3i)(-2 + -3i) = 0 Reorder the terms: (2 + x)(2 + x)(-2 + 3i)(-2 + -3i) = 0 Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x))(-2 + 3i)(-2 + -3i) = 0 ((2 * 2 + x * 2) + x(2 + x))(-2 + 3i)(-2 + -3i) = 0 ((4 + 2x) + x(2 + x))(-2 + 3i)(-2 + -3i) = 0 (4 + 2x + (2 * x + x * x))(-2 + 3i)(-2 + -3i) = 0 (4 + 2x + (2x + x2))(-2 + 3i)(-2 + -3i) = 0 Combine like terms: 2x + 2x = 4x (4 + 4x + x2)(-2 + 3i)(-2 + -3i) = 0 Multiply (4 + 4x + x2) * (-2 + 3i) (4(-2 + 3i) + 4x * (-2 + 3i) + x2(-2 + 3i))(-2 + -3i) = 0 ((-2 * 4 + 3i * 4) + 4x * (-2 + 3i) + x2(-2 + 3i))(-2 + -3i) = 0 ((-8 + 12i) + 4x * (-2 + 3i) + x2(-2 + 3i))(-2 + -3i) = 0 (-8 + 12i + (-2 * 4x + 3i * 4x) + x2(-2 + 3i))(-2 + -3i) = 0 Reorder the terms: (-8 + 12i + (12ix + -8x) + x2(-2 + 3i))(-2 + -3i) = 0 (-8 + 12i + (12ix + -8x) + x2(-2 + 3i))(-2 + -3i) = 0 (-8 + 12i + 12ix + -8x + (-2 * x2 + 3i * x2))(-2 + -3i) = 0 Reorder the terms: (-8 + 12i + 12ix + -8x + (3ix2 + -2x2))(-2 + -3i) = 0 (-8 + 12i + 12ix + -8x + (3ix2 + -2x2))(-2 + -3i) = 0 Reorder the terms: (-8 + 12i + 12ix + 3ix2 + -8x + -2x2)(-2 + -3i) = 0 (-8 + 12i + 12ix + 3ix2 + -8x + -2x2)(-2 + -3i) = 0 Multiply (-8 + 12i + 12ix + 3ix2 + -8x + -2x2) * (-2 + -3i) (-8(-2 + -3i) + 12i * (-2 + -3i) + 12ix * (-2 + -3i) + 3ix2 * (-2 + -3i) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 ((-2 * -8 + -3i * -8) + 12i * (-2 + -3i) + 12ix * (-2 + -3i) + 3ix2 * (-2 + -3i) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 ((16 + 24i) + 12i * (-2 + -3i) + 12ix * (-2 + -3i) + 3ix2 * (-2 + -3i) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + (-2 * 12i + -3i * 12i) + 12ix * (-2 + -3i) + 3ix2 * (-2 + -3i) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + (-24i + -36i2) + 12ix * (-2 + -3i) + 3ix2 * (-2 + -3i) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + -24i + -36i2 + (-2 * 12ix + -3i * 12ix) + 3ix2 * (-2 + -3i) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + -24i + -36i2 + (-24ix + -36i2x) + 3ix2 * (-2 + -3i) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + -24i + -36i2 + -24ix + -36i2x + (-2 * 3ix2 + -3i * 3ix2) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + -24i + -36i2 + -24ix + -36i2x + (-6ix2 + -9i2x2) + -8x * (-2 + -3i) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + -24i + -36i2 + -24ix + -36i2x + -6ix2 + -9i2x2 + (-2 * -8x + -3i * -8x) + -2x2 * (-2 + -3i)) = 0 Reorder the terms: (16 + 24i + -24i + -36i2 + -24ix + -36i2x + -6ix2 + -9i2x2 + (24ix + 16x) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + -24i + -36i2 + -24ix + -36i2x + -6ix2 + -9i2x2 + (24ix + 16x) + -2x2 * (-2 + -3i)) = 0 (16 + 24i + -24i + -36i2 + -24ix + -36i2x + -6ix2 + -9i2x2 + 24ix + 16x + (-2 * -2x2 + -3i * -2x2)) = 0 Reorder the terms: (16 + 24i + -24i + -36i2 + -24ix + -36i2x + -6ix2 + -9i2x2 + 24ix + 16x + (6ix2 + 4x2)) = 0 (16 + 24i + -24i + -36i2 + -24ix + -36i2x + -6ix2 + -9i2x2 + 24ix + 16x + (6ix2 + 4x2)) = 0 Reorder the terms: (16 + 24i + -24i + -24ix + 24ix + -6ix2 + 6ix2 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2) = 0 Combine like terms: 24i + -24i = 0 (16 + 0 + -24ix + 24ix + -6ix2 + 6ix2 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2) = 0 (16 + -24ix + 24ix + -6ix2 + 6ix2 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2) = 0 Combine like terms: -24ix + 24ix = 0 (16 + 0 + -6ix2 + 6ix2 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2) = 0 (16 + -6ix2 + 6ix2 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2) = 0 Combine like terms: -6ix2 + 6ix2 = 0 (16 + 0 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2) = 0 (16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2) = 0 Solving 16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -36i2 + -36i2x + -9i2x2 + 16x + -16 + 4x2 = 0 + -16 Reorder the terms: 16 + -16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = 0 + -16 -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = -16 Add '-16x' to each side of the equation. -36i2 + -36i2x + -9i2x2 + 16x + -16x + 4x2 = -16 + -16x Combine like terms: 16x + -16x = 0 -36i2 + -36i2x + -9i2x2 + 0 + 4x2 = -16 + -16x -36i2 + -36i2x + -9i2x2 + 4x2 = -16 + -16x Add '-4x2' to each side of the equation. -36i2 + -36i2x + -9i2x2 + 4x2 + -4x2 = -16 + -16x + -4x2 Combine like terms: 4x2 + -4x2 = 0 -36i2 + -36i2x + -9i2x2 + 0 = -16 + -16x + -4x2 -36i2 + -36i2x + -9i2x2 = -16 + -16x + -4x2 Reorder the terms: 16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = -16 + -16x + -4x2 + 16 + 16x + 4x2 Reorder the terms: 16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = -16 + 16 + -16x + 16x + -4x2 + 4x2 Combine like terms: -16 + 16 = 0 16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = 0 + -16x + 16x + -4x2 + 4x2 16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = -16x + 16x + -4x2 + 4x2 Combine like terms: -16x + 16x = 0 16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = 0 + -4x2 + 4x2 16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 16 + -36i2 + -36i2x + -9i2x2 + 16x + 4x2 = 0 The solution to this equation could not be determined.
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