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Simplifying (x + 4)(x + -3 + 2i)(x + -3 + -2i) = 0 Reorder the terms: (4 + x)(x + -3 + 2i)(x + -3 + -2i) = 0 Reorder the terms: (4 + x)(-3 + 2i + x)(x + -3 + -2i) = 0 Reorder the terms: (4 + x)(-3 + 2i + x)(-3 + -2i + x) = 0 Multiply (4 + x) * (-3 + 2i + x) (4(-3 + 2i + x) + x(-3 + 2i + x))(-3 + -2i + x) = 0 ((-3 * 4 + 2i * 4 + x * 4) + x(-3 + 2i + x))(-3 + -2i + x) = 0 ((-12 + 8i + 4x) + x(-3 + 2i + x))(-3 + -2i + x) = 0 (-12 + 8i + 4x + (-3 * x + 2i * x + x * x))(-3 + -2i + x) = 0 Reorder the terms: (-12 + 8i + 4x + (2ix + -3x + x2))(-3 + -2i + x) = 0 (-12 + 8i + 4x + (2ix + -3x + x2))(-3 + -2i + x) = 0 Reorder the terms: (-12 + 8i + 2ix + 4x + -3x + x2)(-3 + -2i + x) = 0 Combine like terms: 4x + -3x = 1x (-12 + 8i + 2ix + 1x + x2)(-3 + -2i + x) = 0 Multiply (-12 + 8i + 2ix + 1x + x2) * (-3 + -2i + x) (-12(-3 + -2i + x) + 8i * (-3 + -2i + x) + 2ix * (-3 + -2i + x) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 ((-3 * -12 + -2i * -12 + x * -12) + 8i * (-3 + -2i + x) + 2ix * (-3 + -2i + x) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 ((36 + 24i + -12x) + 8i * (-3 + -2i + x) + 2ix * (-3 + -2i + x) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (36 + 24i + -12x + (-3 * 8i + -2i * 8i + x * 8i) + 2ix * (-3 + -2i + x) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 Reorder the terms: (36 + 24i + -12x + (-24i + 8ix + -16i2) + 2ix * (-3 + -2i + x) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (36 + 24i + -12x + (-24i + 8ix + -16i2) + 2ix * (-3 + -2i + x) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (36 + 24i + -12x + -24i + 8ix + -16i2 + (-3 * 2ix + -2i * 2ix + x * 2ix) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 Reorder the terms: (36 + 24i + -12x + -24i + 8ix + -16i2 + (-6ix + 2ix2 + -4i2x) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (36 + 24i + -12x + -24i + 8ix + -16i2 + (-6ix + 2ix2 + -4i2x) + 1x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (36 + 24i + -12x + -24i + 8ix + -16i2 + -6ix + 2ix2 + -4i2x + (-3 * 1x + -2i * 1x + x * 1x) + x2(-3 + -2i + x)) = 0 Reorder the terms: (36 + 24i + -12x + -24i + 8ix + -16i2 + -6ix + 2ix2 + -4i2x + (-2ix + -3x + 1x2) + x2(-3 + -2i + x)) = 0 (36 + 24i + -12x + -24i + 8ix + -16i2 + -6ix + 2ix2 + -4i2x + (-2ix + -3x + 1x2) + x2(-3 + -2i + x)) = 0 (36 + 24i + -12x + -24i + 8ix + -16i2 + -6ix + 2ix2 + -4i2x + -2ix + -3x + 1x2 + (-3 * x2 + -2i * x2 + x * x2)) = 0 Reorder the terms: (36 + 24i + -12x + -24i + 8ix + -16i2 + -6ix + 2ix2 + -4i2x + -2ix + -3x + 1x2 + (-2ix2 + -3x2 + x3)) = 0 (36 + 24i + -12x + -24i + 8ix + -16i2 + -6ix + 2ix2 + -4i2x + -2ix + -3x + 1x2 + (-2ix2 + -3x2 + x3)) = 0 Reorder the terms: (36 + 24i + -24i + 8ix + -6ix + -2ix + 2ix2 + -2ix2 + -16i2 + -4i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0 Combine like terms: 24i + -24i = 0 (36 + 0 + 8ix + -6ix + -2ix + 2ix2 + -2ix2 + -16i2 + -4i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0 (36 + 8ix + -6ix + -2ix + 2ix2 + -2ix2 + -16i2 + -4i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0 Combine like terms: 8ix + -6ix = 2ix (36 + 2ix + -2ix + 2ix2 + -2ix2 + -16i2 + -4i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0 Combine like terms: 2ix + -2ix = 0 (36 + 0 + 2ix2 + -2ix2 + -16i2 + -4i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0 (36 + 2ix2 + -2ix2 + -16i2 + -4i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0 Combine like terms: 2ix2 + -2ix2 = 0 (36 + 0 + -16i2 + -4i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0 (36 + -16i2 + -4i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0 Combine like terms: -12x + -3x = -15x (36 + -16i2 + -4i2x + -15x + 1x2 + -3x2 + x3) = 0 Combine like terms: 1x2 + -3x2 = -2x2 (36 + -16i2 + -4i2x + -15x + -2x2 + x3) = 0 Solving 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -16i2 + -4i2x + -15x + -2x2 + -36 + x3 = 0 + -36 Reorder the terms: 36 + -36 + -16i2 + -4i2x + -15x + -2x2 + x3 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -16i2 + -4i2x + -15x + -2x2 + x3 = 0 + -36 -16i2 + -4i2x + -15x + -2x2 + x3 = 0 + -36 Combine like terms: 0 + -36 = -36 -16i2 + -4i2x + -15x + -2x2 + x3 = -36 Add '15x' to each side of the equation. -16i2 + -4i2x + -15x + -2x2 + 15x + x3 = -36 + 15x Reorder the terms: -16i2 + -4i2x + -15x + 15x + -2x2 + x3 = -36 + 15x Combine like terms: -15x + 15x = 0 -16i2 + -4i2x + 0 + -2x2 + x3 = -36 + 15x -16i2 + -4i2x + -2x2 + x3 = -36 + 15x Add '2x2' to each side of the equation. -16i2 + -4i2x + -2x2 + 2x2 + x3 = -36 + 15x + 2x2 Combine like terms: -2x2 + 2x2 = 0 -16i2 + -4i2x + 0 + x3 = -36 + 15x + 2x2 -16i2 + -4i2x + x3 = -36 + 15x + 2x2 Add '-1x3' to each side of the equation. -16i2 + -4i2x + x3 + -1x3 = -36 + 15x + 2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -16i2 + -4i2x + 0 = -36 + 15x + 2x2 + -1x3 -16i2 + -4i2x = -36 + 15x + 2x2 + -1x3 Reorder the terms: 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = -36 + 15x + 2x2 + -1x3 + 36 + -15x + -2x2 + x3 Reorder the terms: 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = -36 + 36 + 15x + -15x + 2x2 + -2x2 + -1x3 + x3 Combine like terms: -36 + 36 = 0 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = 0 + 15x + -15x + 2x2 + -2x2 + -1x3 + x3 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = 15x + -15x + 2x2 + -2x2 + -1x3 + x3 Combine like terms: 15x + -15x = 0 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = 0 + 2x2 + -2x2 + -1x3 + x3 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = 2x2 + -2x2 + -1x3 + x3 Combine like terms: 2x2 + -2x2 = 0 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = 0 + -1x3 + x3 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 36 + -16i2 + -4i2x + -15x + -2x2 + x3 = 0 The solution to this equation could not be determined.
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