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Simplifying (x + 3)(x + 4 + -1i)(x + 4 + i) = 0 Reorder the terms: (3 + x)(x + 4 + -1i)(x + 4 + i) = 0 Reorder the terms: (3 + x)(4 + -1i + x)(x + 4 + i) = 0 Reorder the terms: (3 + x)(4 + -1i + x)(4 + i + x) = 0 Multiply (3 + x) * (4 + -1i + x) (3(4 + -1i + x) + x(4 + -1i + x))(4 + i + x) = 0 ((4 * 3 + -1i * 3 + x * 3) + x(4 + -1i + x))(4 + i + x) = 0 ((12 + -3i + 3x) + x(4 + -1i + x))(4 + i + x) = 0 (12 + -3i + 3x + (4 * x + -1i * x + x * x))(4 + i + x) = 0 Reorder the terms: (12 + -3i + 3x + (-1ix + 4x + x2))(4 + i + x) = 0 (12 + -3i + 3x + (-1ix + 4x + x2))(4 + i + x) = 0 Reorder the terms: (12 + -3i + -1ix + 3x + 4x + x2)(4 + i + x) = 0 Combine like terms: 3x + 4x = 7x (12 + -3i + -1ix + 7x + x2)(4 + i + x) = 0 Multiply (12 + -3i + -1ix + 7x + x2) * (4 + i + x) (12(4 + i + x) + -3i * (4 + i + x) + -1ix * (4 + i + x) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 ((4 * 12 + i * 12 + x * 12) + -3i * (4 + i + x) + -1ix * (4 + i + x) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 ((48 + 12i + 12x) + -3i * (4 + i + x) + -1ix * (4 + i + x) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 (48 + 12i + 12x + (4 * -3i + i * -3i + x * -3i) + -1ix * (4 + i + x) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 Reorder the terms: (48 + 12i + 12x + (-12i + -3ix + -3i2) + -1ix * (4 + i + x) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 (48 + 12i + 12x + (-12i + -3ix + -3i2) + -1ix * (4 + i + x) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 (48 + 12i + 12x + -12i + -3ix + -3i2 + (4 * -1ix + i * -1ix + x * -1ix) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 Reorder the terms: (48 + 12i + 12x + -12i + -3ix + -3i2 + (-4ix + -1ix2 + -1i2x) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 (48 + 12i + 12x + -12i + -3ix + -3i2 + (-4ix + -1ix2 + -1i2x) + 7x * (4 + i + x) + x2(4 + i + x)) = 0 (48 + 12i + 12x + -12i + -3ix + -3i2 + -4ix + -1ix2 + -1i2x + (4 * 7x + i * 7x + x * 7x) + x2(4 + i + x)) = 0 Reorder the terms: (48 + 12i + 12x + -12i + -3ix + -3i2 + -4ix + -1ix2 + -1i2x + (7ix + 28x + 7x2) + x2(4 + i + x)) = 0 (48 + 12i + 12x + -12i + -3ix + -3i2 + -4ix + -1ix2 + -1i2x + (7ix + 28x + 7x2) + x2(4 + i + x)) = 0 (48 + 12i + 12x + -12i + -3ix + -3i2 + -4ix + -1ix2 + -1i2x + 7ix + 28x + 7x2 + (4 * x2 + i * x2 + x * x2)) = 0 Reorder the terms: (48 + 12i + 12x + -12i + -3ix + -3i2 + -4ix + -1ix2 + -1i2x + 7ix + 28x + 7x2 + (ix2 + 4x2 + x3)) = 0 (48 + 12i + 12x + -12i + -3ix + -3i2 + -4ix + -1ix2 + -1i2x + 7ix + 28x + 7x2 + (ix2 + 4x2 + x3)) = 0 Reorder the terms: (48 + 12i + -12i + -3ix + -4ix + 7ix + -1ix2 + ix2 + -3i2 + -1i2x + 12x + 28x + 7x2 + 4x2 + x3) = 0 Combine like terms: 12i + -12i = 0 (48 + 0 + -3ix + -4ix + 7ix + -1ix2 + ix2 + -3i2 + -1i2x + 12x + 28x + 7x2 + 4x2 + x3) = 0 (48 + -3ix + -4ix + 7ix + -1ix2 + ix2 + -3i2 + -1i2x + 12x + 28x + 7x2 + 4x2 + x3) = 0 Combine like terms: -3ix + -4ix = -7ix (48 + -7ix + 7ix + -1ix2 + ix2 + -3i2 + -1i2x + 12x + 28x + 7x2 + 4x2 + x3) = 0 Combine like terms: -7ix + 7ix = 0 (48 + 0 + -1ix2 + ix2 + -3i2 + -1i2x + 12x + 28x + 7x2 + 4x2 + x3) = 0 (48 + -1ix2 + ix2 + -3i2 + -1i2x + 12x + 28x + 7x2 + 4x2 + x3) = 0 Combine like terms: -1ix2 + ix2 = 0 (48 + 0 + -3i2 + -1i2x + 12x + 28x + 7x2 + 4x2 + x3) = 0 (48 + -3i2 + -1i2x + 12x + 28x + 7x2 + 4x2 + x3) = 0 Combine like terms: 12x + 28x = 40x (48 + -3i2 + -1i2x + 40x + 7x2 + 4x2 + x3) = 0 Combine like terms: 7x2 + 4x2 = 11x2 (48 + -3i2 + -1i2x + 40x + 11x2 + x3) = 0 Solving 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -3i2 + -1i2x + 40x + 11x2 + -48 + x3 = 0 + -48 Reorder the terms: 48 + -48 + -3i2 + -1i2x + 40x + 11x2 + x3 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -3i2 + -1i2x + 40x + 11x2 + x3 = 0 + -48 -3i2 + -1i2x + 40x + 11x2 + x3 = 0 + -48 Combine like terms: 0 + -48 = -48 -3i2 + -1i2x + 40x + 11x2 + x3 = -48 Add '-40x' to each side of the equation. -3i2 + -1i2x + 40x + 11x2 + -40x + x3 = -48 + -40x Reorder the terms: -3i2 + -1i2x + 40x + -40x + 11x2 + x3 = -48 + -40x Combine like terms: 40x + -40x = 0 -3i2 + -1i2x + 0 + 11x2 + x3 = -48 + -40x -3i2 + -1i2x + 11x2 + x3 = -48 + -40x Add '-11x2' to each side of the equation. -3i2 + -1i2x + 11x2 + -11x2 + x3 = -48 + -40x + -11x2 Combine like terms: 11x2 + -11x2 = 0 -3i2 + -1i2x + 0 + x3 = -48 + -40x + -11x2 -3i2 + -1i2x + x3 = -48 + -40x + -11x2 Add '-1x3' to each side of the equation. -3i2 + -1i2x + x3 + -1x3 = -48 + -40x + -11x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -3i2 + -1i2x + 0 = -48 + -40x + -11x2 + -1x3 -3i2 + -1i2x = -48 + -40x + -11x2 + -1x3 Reorder the terms: 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = -48 + -40x + -11x2 + -1x3 + 48 + 40x + 11x2 + x3 Reorder the terms: 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = -48 + 48 + -40x + 40x + -11x2 + 11x2 + -1x3 + x3 Combine like terms: -48 + 48 = 0 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = 0 + -40x + 40x + -11x2 + 11x2 + -1x3 + x3 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = -40x + 40x + -11x2 + 11x2 + -1x3 + x3 Combine like terms: -40x + 40x = 0 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = 0 + -11x2 + 11x2 + -1x3 + x3 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = -11x2 + 11x2 + -1x3 + x3 Combine like terms: -11x2 + 11x2 = 0 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = 0 + -1x3 + x3 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 48 + -3i2 + -1i2x + 40x + 11x2 + x3 = 0 The solution to this equation could not be determined.
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