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Simplifying (x + 7)(x + -3 + 2i)(x + -3 + -2i) = 0 Reorder the terms: (7 + x)(x + -3 + 2i)(x + -3 + -2i) = 0 Reorder the terms: (7 + x)(-3 + 2i + x)(x + -3 + -2i) = 0 Reorder the terms: (7 + x)(-3 + 2i + x)(-3 + -2i + x) = 0 Multiply (7 + x) * (-3 + 2i + x) (7(-3 + 2i + x) + x(-3 + 2i + x))(-3 + -2i + x) = 0 ((-3 * 7 + 2i * 7 + x * 7) + x(-3 + 2i + x))(-3 + -2i + x) = 0 ((-21 + 14i + 7x) + x(-3 + 2i + x))(-3 + -2i + x) = 0 (-21 + 14i + 7x + (-3 * x + 2i * x + x * x))(-3 + -2i + x) = 0 Reorder the terms: (-21 + 14i + 7x + (2ix + -3x + x2))(-3 + -2i + x) = 0 (-21 + 14i + 7x + (2ix + -3x + x2))(-3 + -2i + x) = 0 Reorder the terms: (-21 + 14i + 2ix + 7x + -3x + x2)(-3 + -2i + x) = 0 Combine like terms: 7x + -3x = 4x (-21 + 14i + 2ix + 4x + x2)(-3 + -2i + x) = 0 Multiply (-21 + 14i + 2ix + 4x + x2) * (-3 + -2i + x) (-21(-3 + -2i + x) + 14i * (-3 + -2i + x) + 2ix * (-3 + -2i + x) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 ((-3 * -21 + -2i * -21 + x * -21) + 14i * (-3 + -2i + x) + 2ix * (-3 + -2i + x) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 ((63 + 42i + -21x) + 14i * (-3 + -2i + x) + 2ix * (-3 + -2i + x) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (63 + 42i + -21x + (-3 * 14i + -2i * 14i + x * 14i) + 2ix * (-3 + -2i + x) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 Reorder the terms: (63 + 42i + -21x + (-42i + 14ix + -28i2) + 2ix * (-3 + -2i + x) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (63 + 42i + -21x + (-42i + 14ix + -28i2) + 2ix * (-3 + -2i + x) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (63 + 42i + -21x + -42i + 14ix + -28i2 + (-3 * 2ix + -2i * 2ix + x * 2ix) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 Reorder the terms: (63 + 42i + -21x + -42i + 14ix + -28i2 + (-6ix + 2ix2 + -4i2x) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (63 + 42i + -21x + -42i + 14ix + -28i2 + (-6ix + 2ix2 + -4i2x) + 4x * (-3 + -2i + x) + x2(-3 + -2i + x)) = 0 (63 + 42i + -21x + -42i + 14ix + -28i2 + -6ix + 2ix2 + -4i2x + (-3 * 4x + -2i * 4x + x * 4x) + x2(-3 + -2i + x)) = 0 Reorder the terms: (63 + 42i + -21x + -42i + 14ix + -28i2 + -6ix + 2ix2 + -4i2x + (-8ix + -12x + 4x2) + x2(-3 + -2i + x)) = 0 (63 + 42i + -21x + -42i + 14ix + -28i2 + -6ix + 2ix2 + -4i2x + (-8ix + -12x + 4x2) + x2(-3 + -2i + x)) = 0 (63 + 42i + -21x + -42i + 14ix + -28i2 + -6ix + 2ix2 + -4i2x + -8ix + -12x + 4x2 + (-3 * x2 + -2i * x2 + x * x2)) = 0 Reorder the terms: (63 + 42i + -21x + -42i + 14ix + -28i2 + -6ix + 2ix2 + -4i2x + -8ix + -12x + 4x2 + (-2ix2 + -3x2 + x3)) = 0 (63 + 42i + -21x + -42i + 14ix + -28i2 + -6ix + 2ix2 + -4i2x + -8ix + -12x + 4x2 + (-2ix2 + -3x2 + x3)) = 0 Reorder the terms: (63 + 42i + -42i + 14ix + -6ix + -8ix + 2ix2 + -2ix2 + -28i2 + -4i2x + -21x + -12x + 4x2 + -3x2 + x3) = 0 Combine like terms: 42i + -42i = 0 (63 + 0 + 14ix + -6ix + -8ix + 2ix2 + -2ix2 + -28i2 + -4i2x + -21x + -12x + 4x2 + -3x2 + x3) = 0 (63 + 14ix + -6ix + -8ix + 2ix2 + -2ix2 + -28i2 + -4i2x + -21x + -12x + 4x2 + -3x2 + x3) = 0 Combine like terms: 14ix + -6ix = 8ix (63 + 8ix + -8ix + 2ix2 + -2ix2 + -28i2 + -4i2x + -21x + -12x + 4x2 + -3x2 + x3) = 0 Combine like terms: 8ix + -8ix = 0 (63 + 0 + 2ix2 + -2ix2 + -28i2 + -4i2x + -21x + -12x + 4x2 + -3x2 + x3) = 0 (63 + 2ix2 + -2ix2 + -28i2 + -4i2x + -21x + -12x + 4x2 + -3x2 + x3) = 0 Combine like terms: 2ix2 + -2ix2 = 0 (63 + 0 + -28i2 + -4i2x + -21x + -12x + 4x2 + -3x2 + x3) = 0 (63 + -28i2 + -4i2x + -21x + -12x + 4x2 + -3x2 + x3) = 0 Combine like terms: -21x + -12x = -33x (63 + -28i2 + -4i2x + -33x + 4x2 + -3x2 + x3) = 0 Combine like terms: 4x2 + -3x2 = 1x2 (63 + -28i2 + -4i2x + -33x + 1x2 + x3) = 0 Solving 63 + -28i2 + -4i2x + -33x + 1x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-63' to each side of the equation. 63 + -28i2 + -4i2x + -33x + 1x2 + -63 + x3 = 0 + -63 Reorder the terms: 63 + -63 + -28i2 + -4i2x + -33x + 1x2 + x3 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -28i2 + -4i2x + -33x + 1x2 + x3 = 0 + -63 -28i2 + -4i2x + -33x + 1x2 + x3 = 0 + -63 Combine like terms: 0 + -63 = -63 -28i2 + -4i2x + -33x + 1x2 + x3 = -63 Add '33x' to each side of the equation. -28i2 + -4i2x + -33x + 1x2 + 33x + x3 = -63 + 33x Reorder the terms: -28i2 + -4i2x + -33x + 33x + 1x2 + x3 = -63 + 33x Combine like terms: -33x + 33x = 0 -28i2 + -4i2x + 0 + 1x2 + x3 = -63 + 33x -28i2 + -4i2x + 1x2 + x3 = -63 + 33x Add '-1x2' to each side of the equation. -28i2 + -4i2x + 1x2 + -1x2 + x3 = -63 + 33x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -28i2 + -4i2x + 0 + x3 = -63 + 33x + -1x2 -28i2 + -4i2x + x3 = -63 + 33x + -1x2 Add '-1x3' to each side of the equation. -28i2 + -4i2x + x3 + -1x3 = -63 + 33x + -1x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -28i2 + -4i2x + 0 = -63 + 33x + -1x2 + -1x3 -28i2 + -4i2x = -63 + 33x + -1x2 + -1x3 Reorder the terms: 63 + -28i2 + -4i2x + -33x + x2 + x3 = -63 + 33x + -1x2 + -1x3 + 63 + -33x + x2 + x3 Reorder the terms: 63 + -28i2 + -4i2x + -33x + x2 + x3 = -63 + 63 + 33x + -33x + -1x2 + x2 + -1x3 + x3 Combine like terms: -63 + 63 = 0 63 + -28i2 + -4i2x + -33x + x2 + x3 = 0 + 33x + -33x + -1x2 + x2 + -1x3 + x3 63 + -28i2 + -4i2x + -33x + x2 + x3 = 33x + -33x + -1x2 + x2 + -1x3 + x3 Combine like terms: 33x + -33x = 0 63 + -28i2 + -4i2x + -33x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3 63 + -28i2 + -4i2x + -33x + x2 + x3 = -1x2 + x2 + -1x3 + x3 Combine like terms: -1x2 + x2 = 0 63 + -28i2 + -4i2x + -33x + x2 + x3 = 0 + -1x3 + x3 63 + -28i2 + -4i2x + -33x + x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 63 + -28i2 + -4i2x + -33x + x2 + x3 = 0 The solution to this equation could not be determined.
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