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Simplifying (x + -5)(x + 4 + i)(x + 4 + -1i) = 0 Reorder the terms: (-5 + x)(x + 4 + i)(x + 4 + -1i) = 0 Reorder the terms: (-5 + x)(4 + i + x)(x + 4 + -1i) = 0 Reorder the terms: (-5 + x)(4 + i + x)(4 + -1i + x) = 0 Multiply (-5 + x) * (4 + i + x) (-5(4 + i + x) + x(4 + i + x))(4 + -1i + x) = 0 ((4 * -5 + i * -5 + x * -5) + x(4 + i + x))(4 + -1i + x) = 0 ((-20 + -5i + -5x) + x(4 + i + x))(4 + -1i + x) = 0 (-20 + -5i + -5x + (4 * x + i * x + x * x))(4 + -1i + x) = 0 Reorder the terms: (-20 + -5i + -5x + (ix + 4x + x2))(4 + -1i + x) = 0 (-20 + -5i + -5x + (ix + 4x + x2))(4 + -1i + x) = 0 Reorder the terms: (-20 + -5i + ix + -5x + 4x + x2)(4 + -1i + x) = 0 Combine like terms: -5x + 4x = -1x (-20 + -5i + ix + -1x + x2)(4 + -1i + x) = 0 Multiply (-20 + -5i + ix + -1x + x2) * (4 + -1i + x) (-20(4 + -1i + x) + -5i * (4 + -1i + x) + ix(4 + -1i + x) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 ((4 * -20 + -1i * -20 + x * -20) + -5i * (4 + -1i + x) + ix(4 + -1i + x) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 ((-80 + 20i + -20x) + -5i * (4 + -1i + x) + ix(4 + -1i + x) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 (-80 + 20i + -20x + (4 * -5i + -1i * -5i + x * -5i) + ix(4 + -1i + x) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 Reorder the terms: (-80 + 20i + -20x + (-20i + -5ix + 5i2) + ix(4 + -1i + x) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 (-80 + 20i + -20x + (-20i + -5ix + 5i2) + ix(4 + -1i + x) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 (-80 + 20i + -20x + -20i + -5ix + 5i2 + (4 * ix + -1i * ix + x * ix) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 Reorder the terms: (-80 + 20i + -20x + -20i + -5ix + 5i2 + (4ix + ix2 + -1i2x) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 (-80 + 20i + -20x + -20i + -5ix + 5i2 + (4ix + ix2 + -1i2x) + -1x * (4 + -1i + x) + x2(4 + -1i + x)) = 0 (-80 + 20i + -20x + -20i + -5ix + 5i2 + 4ix + ix2 + -1i2x + (4 * -1x + -1i * -1x + x * -1x) + x2(4 + -1i + x)) = 0 Reorder the terms: (-80 + 20i + -20x + -20i + -5ix + 5i2 + 4ix + ix2 + -1i2x + (1ix + -4x + -1x2) + x2(4 + -1i + x)) = 0 (-80 + 20i + -20x + -20i + -5ix + 5i2 + 4ix + ix2 + -1i2x + (1ix + -4x + -1x2) + x2(4 + -1i + x)) = 0 (-80 + 20i + -20x + -20i + -5ix + 5i2 + 4ix + ix2 + -1i2x + 1ix + -4x + -1x2 + (4 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-80 + 20i + -20x + -20i + -5ix + 5i2 + 4ix + ix2 + -1i2x + 1ix + -4x + -1x2 + (-1ix2 + 4x2 + x3)) = 0 (-80 + 20i + -20x + -20i + -5ix + 5i2 + 4ix + ix2 + -1i2x + 1ix + -4x + -1x2 + (-1ix2 + 4x2 + x3)) = 0 Reorder the terms: (-80 + 20i + -20i + -5ix + 4ix + 1ix + ix2 + -1ix2 + 5i2 + -1i2x + -20x + -4x + -1x2 + 4x2 + x3) = 0 Combine like terms: 20i + -20i = 0 (-80 + 0 + -5ix + 4ix + 1ix + ix2 + -1ix2 + 5i2 + -1i2x + -20x + -4x + -1x2 + 4x2 + x3) = 0 (-80 + -5ix + 4ix + 1ix + ix2 + -1ix2 + 5i2 + -1i2x + -20x + -4x + -1x2 + 4x2 + x3) = 0 Combine like terms: -5ix + 4ix = -1ix (-80 + -1ix + 1ix + ix2 + -1ix2 + 5i2 + -1i2x + -20x + -4x + -1x2 + 4x2 + x3) = 0 Combine like terms: -1ix + 1ix = 0 (-80 + 0 + ix2 + -1ix2 + 5i2 + -1i2x + -20x + -4x + -1x2 + 4x2 + x3) = 0 (-80 + ix2 + -1ix2 + 5i2 + -1i2x + -20x + -4x + -1x2 + 4x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (-80 + 0 + 5i2 + -1i2x + -20x + -4x + -1x2 + 4x2 + x3) = 0 (-80 + 5i2 + -1i2x + -20x + -4x + -1x2 + 4x2 + x3) = 0 Combine like terms: -20x + -4x = -24x (-80 + 5i2 + -1i2x + -24x + -1x2 + 4x2 + x3) = 0 Combine like terms: -1x2 + 4x2 = 3x2 (-80 + 5i2 + -1i2x + -24x + 3x2 + x3) = 0 Solving -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 5i2 + -1i2x + -24x + 3x2 + 80 + x3 = 0 + 80 Reorder the terms: -80 + 80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 5i2 + -1i2x + -24x + 3x2 + x3 = 0 + 80 5i2 + -1i2x + -24x + 3x2 + x3 = 0 + 80 Combine like terms: 0 + 80 = 80 5i2 + -1i2x + -24x + 3x2 + x3 = 80 Add '24x' to each side of the equation. 5i2 + -1i2x + -24x + 3x2 + 24x + x3 = 80 + 24x Reorder the terms: 5i2 + -1i2x + -24x + 24x + 3x2 + x3 = 80 + 24x Combine like terms: -24x + 24x = 0 5i2 + -1i2x + 0 + 3x2 + x3 = 80 + 24x 5i2 + -1i2x + 3x2 + x3 = 80 + 24x Add '-3x2' to each side of the equation. 5i2 + -1i2x + 3x2 + -3x2 + x3 = 80 + 24x + -3x2 Combine like terms: 3x2 + -3x2 = 0 5i2 + -1i2x + 0 + x3 = 80 + 24x + -3x2 5i2 + -1i2x + x3 = 80 + 24x + -3x2 Add '-1x3' to each side of the equation. 5i2 + -1i2x + x3 + -1x3 = 80 + 24x + -3x2 + -1x3 Combine like terms: x3 + -1x3 = 0 5i2 + -1i2x + 0 = 80 + 24x + -3x2 + -1x3 5i2 + -1i2x = 80 + 24x + -3x2 + -1x3 Reorder the terms: -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 80 + 24x + -3x2 + -1x3 + -80 + -24x + 3x2 + x3 Reorder the terms: -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 80 + -80 + 24x + -24x + -3x2 + 3x2 + -1x3 + x3 Combine like terms: 80 + -80 = 0 -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 0 + 24x + -24x + -3x2 + 3x2 + -1x3 + x3 -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 24x + -24x + -3x2 + 3x2 + -1x3 + x3 Combine like terms: 24x + -24x = 0 -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 0 + -3x2 + 3x2 + -1x3 + x3 -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = -3x2 + 3x2 + -1x3 + x3 Combine like terms: -3x2 + 3x2 = 0 -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 0 + -1x3 + x3 -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -80 + 5i2 + -1i2x + -24x + 3x2 + x3 = 0 The solution to this equation could not be determined.
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