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Simplifying (x + 3)(1 + 4i)(1 + -4i) = 0 Reorder the terms: (3 + x)(1 + 4i)(1 + -4i) = 0 Multiply (3 + x) * (1 + 4i) (3(1 + 4i) + x(1 + 4i))(1 + -4i) = 0 ((1 * 3 + 4i * 3) + x(1 + 4i))(1 + -4i) = 0 ((3 + 12i) + x(1 + 4i))(1 + -4i) = 0 (3 + 12i + (1 * x + 4i * x))(1 + -4i) = 0 Reorder the terms: (3 + 12i + (4ix + 1x))(1 + -4i) = 0 (3 + 12i + (4ix + 1x))(1 + -4i) = 0 (3 + 12i + 4ix + 1x)(1 + -4i) = 0 Multiply (3 + 12i + 4ix + 1x) * (1 + -4i) (3(1 + -4i) + 12i * (1 + -4i) + 4ix * (1 + -4i) + 1x * (1 + -4i)) = 0 ((1 * 3 + -4i * 3) + 12i * (1 + -4i) + 4ix * (1 + -4i) + 1x * (1 + -4i)) = 0 ((3 + -12i) + 12i * (1 + -4i) + 4ix * (1 + -4i) + 1x * (1 + -4i)) = 0 (3 + -12i + (1 * 12i + -4i * 12i) + 4ix * (1 + -4i) + 1x * (1 + -4i)) = 0 (3 + -12i + (12i + -48i2) + 4ix * (1 + -4i) + 1x * (1 + -4i)) = 0 (3 + -12i + 12i + -48i2 + (1 * 4ix + -4i * 4ix) + 1x * (1 + -4i)) = 0 (3 + -12i + 12i + -48i2 + (4ix + -16i2x) + 1x * (1 + -4i)) = 0 (3 + -12i + 12i + -48i2 + 4ix + -16i2x + (1 * 1x + -4i * 1x)) = 0 Reorder the terms: (3 + -12i + 12i + -48i2 + 4ix + -16i2x + (-4ix + 1x)) = 0 (3 + -12i + 12i + -48i2 + 4ix + -16i2x + (-4ix + 1x)) = 0 Reorder the terms: (3 + -12i + 12i + 4ix + -4ix + -48i2 + -16i2x + 1x) = 0 Combine like terms: -12i + 12i = 0 (3 + 0 + 4ix + -4ix + -48i2 + -16i2x + 1x) = 0 (3 + 4ix + -4ix + -48i2 + -16i2x + 1x) = 0 Combine like terms: 4ix + -4ix = 0 (3 + 0 + -48i2 + -16i2x + 1x) = 0 (3 + -48i2 + -16i2x + 1x) = 0 Solving 3 + -48i2 + -16i2x + 1x = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -48i2 + -16i2x + -3 + 1x = 0 + -3 Reorder the terms: 3 + -3 + -48i2 + -16i2x + 1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -48i2 + -16i2x + 1x = 0 + -3 -48i2 + -16i2x + 1x = 0 + -3 Combine like terms: 0 + -3 = -3 -48i2 + -16i2x + 1x = -3 Add '-1x' to each side of the equation. -48i2 + -16i2x + 1x + -1x = -3 + -1x Combine like terms: 1x + -1x = 0 -48i2 + -16i2x + 0 = -3 + -1x -48i2 + -16i2x = -3 + -1x Reorder the terms: 3 + -48i2 + -16i2x + x = -3 + -1x + 3 + x Reorder the terms: 3 + -48i2 + -16i2x + x = -3 + 3 + -1x + x Combine like terms: -3 + 3 = 0 3 + -48i2 + -16i2x + x = 0 + -1x + x 3 + -48i2 + -16i2x + x = -1x + x Combine like terms: -1x + x = 0 3 + -48i2 + -16i2x + x = 0 The solution to this equation could not be determined.
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