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Simplifying (x + -5)(x + 4i)(x + -4i) = 0 Reorder the terms: (-5 + x)(x + 4i)(x + -4i) = 0 Reorder the terms: (-5 + x)(4i + x)(x + -4i) = 0 Reorder the terms: (-5 + x)(4i + x)(-4i + x) = 0 Multiply (-5 + x) * (4i + x) (-5(4i + x) + x(4i + x))(-4i + x) = 0 ((4i * -5 + x * -5) + x(4i + x))(-4i + x) = 0 ((-20i + -5x) + x(4i + x))(-4i + x) = 0 (-20i + -5x + (4i * x + x * x))(-4i + x) = 0 (-20i + -5x + (4ix + x2))(-4i + x) = 0 Reorder the terms: (-20i + 4ix + -5x + x2)(-4i + x) = 0 (-20i + 4ix + -5x + x2)(-4i + x) = 0 Multiply (-20i + 4ix + -5x + x2) * (-4i + x) (-20i * (-4i + x) + 4ix * (-4i + x) + -5x * (-4i + x) + x2(-4i + x)) = 0 ((-4i * -20i + x * -20i) + 4ix * (-4i + x) + -5x * (-4i + x) + x2(-4i + x)) = 0 Reorder the terms: ((-20ix + 80i2) + 4ix * (-4i + x) + -5x * (-4i + x) + x2(-4i + x)) = 0 ((-20ix + 80i2) + 4ix * (-4i + x) + -5x * (-4i + x) + x2(-4i + x)) = 0 (-20ix + 80i2 + (-4i * 4ix + x * 4ix) + -5x * (-4i + x) + x2(-4i + x)) = 0 Reorder the terms: (-20ix + 80i2 + (4ix2 + -16i2x) + -5x * (-4i + x) + x2(-4i + x)) = 0 (-20ix + 80i2 + (4ix2 + -16i2x) + -5x * (-4i + x) + x2(-4i + x)) = 0 (-20ix + 80i2 + 4ix2 + -16i2x + (-4i * -5x + x * -5x) + x2(-4i + x)) = 0 (-20ix + 80i2 + 4ix2 + -16i2x + (20ix + -5x2) + x2(-4i + x)) = 0 (-20ix + 80i2 + 4ix2 + -16i2x + 20ix + -5x2 + (-4i * x2 + x * x2)) = 0 (-20ix + 80i2 + 4ix2 + -16i2x + 20ix + -5x2 + (-4ix2 + x3)) = 0 Reorder the terms: (-20ix + 20ix + 4ix2 + -4ix2 + 80i2 + -16i2x + -5x2 + x3) = 0 Combine like terms: -20ix + 20ix = 0 (0 + 4ix2 + -4ix2 + 80i2 + -16i2x + -5x2 + x3) = 0 (4ix2 + -4ix2 + 80i2 + -16i2x + -5x2 + x3) = 0 Combine like terms: 4ix2 + -4ix2 = 0 (0 + 80i2 + -16i2x + -5x2 + x3) = 0 (80i2 + -16i2x + -5x2 + x3) = 0 Solving 80i2 + -16i2x + -5x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5x2' to each side of the equation. 80i2 + -16i2x + -5x2 + 5x2 + x3 = 0 + 5x2 Combine like terms: -5x2 + 5x2 = 0 80i2 + -16i2x + 0 + x3 = 0 + 5x2 80i2 + -16i2x + x3 = 0 + 5x2 Remove the zero: 80i2 + -16i2x + x3 = 5x2 Add '-1x3' to each side of the equation. 80i2 + -16i2x + x3 + -1x3 = 5x2 + -1x3 Combine like terms: x3 + -1x3 = 0 80i2 + -16i2x + 0 = 5x2 + -1x3 80i2 + -16i2x = 5x2 + -1x3 Reorder the terms: 80i2 + -16i2x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3 Combine like terms: 5x2 + -5x2 = 0 80i2 + -16i2x + -5x2 + x3 = 0 + -1x3 + x3 80i2 + -16i2x + -5x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 80i2 + -16i2x + -5x2 + x3 = 0 The solution to this equation could not be determined.
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