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Simplifying (x + 4)(x + -4)(x + 4i)(x + -4i) = 0 Reorder the terms: (4 + x)(x + -4)(x + 4i)(x + -4i) = 0 Reorder the terms: (4 + x)(-4 + x)(x + 4i)(x + -4i) = 0 Reorder the terms: (4 + x)(-4 + x)(4i + x)(x + -4i) = 0 Reorder the terms: (4 + x)(-4 + x)(4i + x)(-4i + x) = 0 Multiply (4 + x) * (-4 + x) (4(-4 + x) + x(-4 + x))(4i + x)(-4i + x) = 0 ((-4 * 4 + x * 4) + x(-4 + x))(4i + x)(-4i + x) = 0 ((-16 + 4x) + x(-4 + x))(4i + x)(-4i + x) = 0 (-16 + 4x + (-4 * x + x * x))(4i + x)(-4i + x) = 0 (-16 + 4x + (-4x + x2))(4i + x)(-4i + x) = 0 Combine like terms: 4x + -4x = 0 (-16 + 0 + x2)(4i + x)(-4i + x) = 0 (-16 + x2)(4i + x)(-4i + x) = 0 Multiply (-16 + x2) * (4i + x) (-16(4i + x) + x2(4i + x))(-4i + x) = 0 ((4i * -16 + x * -16) + x2(4i + x))(-4i + x) = 0 ((-64i + -16x) + x2(4i + x))(-4i + x) = 0 (-64i + -16x + (4i * x2 + x * x2))(-4i + x) = 0 (-64i + -16x + (4ix2 + x3))(-4i + x) = 0 Reorder the terms: (-64i + 4ix2 + -16x + x3)(-4i + x) = 0 (-64i + 4ix2 + -16x + x3)(-4i + x) = 0 Multiply (-64i + 4ix2 + -16x + x3) * (-4i + x) (-64i * (-4i + x) + 4ix2 * (-4i + x) + -16x * (-4i + x) + x3(-4i + x)) = 0 ((-4i * -64i + x * -64i) + 4ix2 * (-4i + x) + -16x * (-4i + x) + x3(-4i + x)) = 0 Reorder the terms: ((-64ix + 256i2) + 4ix2 * (-4i + x) + -16x * (-4i + x) + x3(-4i + x)) = 0 ((-64ix + 256i2) + 4ix2 * (-4i + x) + -16x * (-4i + x) + x3(-4i + x)) = 0 (-64ix + 256i2 + (-4i * 4ix2 + x * 4ix2) + -16x * (-4i + x) + x3(-4i + x)) = 0 Reorder the terms: (-64ix + 256i2 + (4ix3 + -16i2x2) + -16x * (-4i + x) + x3(-4i + x)) = 0 (-64ix + 256i2 + (4ix3 + -16i2x2) + -16x * (-4i + x) + x3(-4i + x)) = 0 (-64ix + 256i2 + 4ix3 + -16i2x2 + (-4i * -16x + x * -16x) + x3(-4i + x)) = 0 (-64ix + 256i2 + 4ix3 + -16i2x2 + (64ix + -16x2) + x3(-4i + x)) = 0 (-64ix + 256i2 + 4ix3 + -16i2x2 + 64ix + -16x2 + (-4i * x3 + x * x3)) = 0 (-64ix + 256i2 + 4ix3 + -16i2x2 + 64ix + -16x2 + (-4ix3 + x4)) = 0 Reorder the terms: (-64ix + 64ix + 4ix3 + -4ix3 + 256i2 + -16i2x2 + -16x2 + x4) = 0 Combine like terms: -64ix + 64ix = 0 (0 + 4ix3 + -4ix3 + 256i2 + -16i2x2 + -16x2 + x4) = 0 (4ix3 + -4ix3 + 256i2 + -16i2x2 + -16x2 + x4) = 0 Combine like terms: 4ix3 + -4ix3 = 0 (0 + 256i2 + -16i2x2 + -16x2 + x4) = 0 (256i2 + -16i2x2 + -16x2 + x4) = 0 Solving 256i2 + -16i2x2 + -16x2 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '16x2' to each side of the equation. 256i2 + -16i2x2 + -16x2 + 16x2 + x4 = 0 + 16x2 Combine like terms: -16x2 + 16x2 = 0 256i2 + -16i2x2 + 0 + x4 = 0 + 16x2 256i2 + -16i2x2 + x4 = 0 + 16x2 Remove the zero: 256i2 + -16i2x2 + x4 = 16x2 Add '-1x4' to each side of the equation. 256i2 + -16i2x2 + x4 + -1x4 = 16x2 + -1x4 Combine like terms: x4 + -1x4 = 0 256i2 + -16i2x2 + 0 = 16x2 + -1x4 256i2 + -16i2x2 = 16x2 + -1x4 Reorder the terms: 256i2 + -16i2x2 + -16x2 + x4 = 16x2 + -16x2 + -1x4 + x4 Combine like terms: 16x2 + -16x2 = 0 256i2 + -16i2x2 + -16x2 + x4 = 0 + -1x4 + x4 256i2 + -16i2x2 + -16x2 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 256i2 + -16i2x2 + -16x2 + x4 = 0 The solution to this equation could not be determined.
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