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Simplifying (x + -4)(x + -4)(x + 2i)(x + -2i) = 0 Reorder the terms: (-4 + x)(x + -4)(x + 2i)(x + -2i) = 0 Reorder the terms: (-4 + x)(-4 + x)(x + 2i)(x + -2i) = 0 Reorder the terms: (-4 + x)(-4 + x)(2i + x)(x + -2i) = 0 Reorder the terms: (-4 + x)(-4 + x)(2i + x)(-2i + x) = 0 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x))(2i + x)(-2i + x) = 0 ((-4 * -4 + x * -4) + x(-4 + x))(2i + x)(-2i + x) = 0 ((16 + -4x) + x(-4 + x))(2i + x)(-2i + x) = 0 (16 + -4x + (-4 * x + x * x))(2i + x)(-2i + x) = 0 (16 + -4x + (-4x + x2))(2i + x)(-2i + x) = 0 Combine like terms: -4x + -4x = -8x (16 + -8x + x2)(2i + x)(-2i + x) = 0 Multiply (16 + -8x + x2) * (2i + x) (16(2i + x) + -8x * (2i + x) + x2(2i + x))(-2i + x) = 0 ((2i * 16 + x * 16) + -8x * (2i + x) + x2(2i + x))(-2i + x) = 0 ((32i + 16x) + -8x * (2i + x) + x2(2i + x))(-2i + x) = 0 (32i + 16x + (2i * -8x + x * -8x) + x2(2i + x))(-2i + x) = 0 (32i + 16x + (-16ix + -8x2) + x2(2i + x))(-2i + x) = 0 (32i + 16x + -16ix + -8x2 + (2i * x2 + x * x2))(-2i + x) = 0 (32i + 16x + -16ix + -8x2 + (2ix2 + x3))(-2i + x) = 0 Reorder the terms: (32i + -16ix + 2ix2 + 16x + -8x2 + x3)(-2i + x) = 0 (32i + -16ix + 2ix2 + 16x + -8x2 + x3)(-2i + x) = 0 Multiply (32i + -16ix + 2ix2 + 16x + -8x2 + x3) * (-2i + x) (32i * (-2i + x) + -16ix * (-2i + x) + 2ix2 * (-2i + x) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 ((-2i * 32i + x * 32i) + -16ix * (-2i + x) + 2ix2 * (-2i + x) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 Reorder the terms: ((32ix + -64i2) + -16ix * (-2i + x) + 2ix2 * (-2i + x) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 ((32ix + -64i2) + -16ix * (-2i + x) + 2ix2 * (-2i + x) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 (32ix + -64i2 + (-2i * -16ix + x * -16ix) + 2ix2 * (-2i + x) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 Reorder the terms: (32ix + -64i2 + (-16ix2 + 32i2x) + 2ix2 * (-2i + x) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 (32ix + -64i2 + (-16ix2 + 32i2x) + 2ix2 * (-2i + x) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 (32ix + -64i2 + -16ix2 + 32i2x + (-2i * 2ix2 + x * 2ix2) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 Reorder the terms: (32ix + -64i2 + -16ix2 + 32i2x + (2ix3 + -4i2x2) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 (32ix + -64i2 + -16ix2 + 32i2x + (2ix3 + -4i2x2) + 16x * (-2i + x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 (32ix + -64i2 + -16ix2 + 32i2x + 2ix3 + -4i2x2 + (-2i * 16x + x * 16x) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 (32ix + -64i2 + -16ix2 + 32i2x + 2ix3 + -4i2x2 + (-32ix + 16x2) + -8x2 * (-2i + x) + x3(-2i + x)) = 0 (32ix + -64i2 + -16ix2 + 32i2x + 2ix3 + -4i2x2 + -32ix + 16x2 + (-2i * -8x2 + x * -8x2) + x3(-2i + x)) = 0 (32ix + -64i2 + -16ix2 + 32i2x + 2ix3 + -4i2x2 + -32ix + 16x2 + (16ix2 + -8x3) + x3(-2i + x)) = 0 (32ix + -64i2 + -16ix2 + 32i2x + 2ix3 + -4i2x2 + -32ix + 16x2 + 16ix2 + -8x3 + (-2i * x3 + x * x3)) = 0 (32ix + -64i2 + -16ix2 + 32i2x + 2ix3 + -4i2x2 + -32ix + 16x2 + 16ix2 + -8x3 + (-2ix3 + x4)) = 0 Reorder the terms: (32ix + -32ix + -16ix2 + 16ix2 + 2ix3 + -2ix3 + -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4) = 0 Combine like terms: 32ix + -32ix = 0 (0 + -16ix2 + 16ix2 + 2ix3 + -2ix3 + -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4) = 0 (-16ix2 + 16ix2 + 2ix3 + -2ix3 + -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4) = 0 Combine like terms: -16ix2 + 16ix2 = 0 (0 + 2ix3 + -2ix3 + -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4) = 0 (2ix3 + -2ix3 + -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4) = 0 Combine like terms: 2ix3 + -2ix3 = 0 (0 + -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4) = 0 (-64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4) = 0 Solving -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + 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. -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + -16x2 + x4 = 0 + -16x2 Reorder the terms: -64i2 + 32i2x + -4i2x2 + 16x2 + -16x2 + -8x3 + x4 = 0 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -64i2 + 32i2x + -4i2x2 + 0 + -8x3 + x4 = 0 + -16x2 -64i2 + 32i2x + -4i2x2 + -8x3 + x4 = 0 + -16x2 Remove the zero: -64i2 + 32i2x + -4i2x2 + -8x3 + x4 = -16x2 Add '8x3' to each side of the equation. -64i2 + 32i2x + -4i2x2 + -8x3 + 8x3 + x4 = -16x2 + 8x3 Combine like terms: -8x3 + 8x3 = 0 -64i2 + 32i2x + -4i2x2 + 0 + x4 = -16x2 + 8x3 -64i2 + 32i2x + -4i2x2 + x4 = -16x2 + 8x3 Add '-1x4' to each side of the equation. -64i2 + 32i2x + -4i2x2 + x4 + -1x4 = -16x2 + 8x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -64i2 + 32i2x + -4i2x2 + 0 = -16x2 + 8x3 + -1x4 -64i2 + 32i2x + -4i2x2 = -16x2 + 8x3 + -1x4 Reorder the terms: -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4 = -16x2 + 16x2 + 8x3 + -8x3 + -1x4 + x4 Combine like terms: -16x2 + 16x2 = 0 -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4 = 0 + 8x3 + -8x3 + -1x4 + x4 -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4 = 8x3 + -8x3 + -1x4 + x4 Combine like terms: 8x3 + -8x3 = 0 -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4 = 0 + -1x4 + x4 -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -64i2 + 32i2x + -4i2x2 + 16x2 + -8x3 + x4 = 0 The solution to this equation could not be determined.
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