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Simplifying (x + -3)(x + 13)(x + -5)(x + -4i) = 0 Reorder the terms: (-3 + x)(x + 13)(x + -5)(x + -4i) = 0 Reorder the terms: (-3 + x)(13 + x)(x + -5)(x + -4i) = 0 Reorder the terms: (-3 + x)(13 + x)(-5 + x)(x + -4i) = 0 Reorder the terms: (-3 + x)(13 + x)(-5 + x)(-4i + x) = 0 Multiply (-3 + x) * (13 + x) (-3(13 + x) + x(13 + x))(-5 + x)(-4i + x) = 0 ((13 * -3 + x * -3) + x(13 + x))(-5 + x)(-4i + x) = 0 ((-39 + -3x) + x(13 + x))(-5 + x)(-4i + x) = 0 (-39 + -3x + (13 * x + x * x))(-5 + x)(-4i + x) = 0 (-39 + -3x + (13x + x2))(-5 + x)(-4i + x) = 0 Combine like terms: -3x + 13x = 10x (-39 + 10x + x2)(-5 + x)(-4i + x) = 0 Multiply (-39 + 10x + x2) * (-5 + x) (-39(-5 + x) + 10x * (-5 + x) + x2(-5 + x))(-4i + x) = 0 ((-5 * -39 + x * -39) + 10x * (-5 + x) + x2(-5 + x))(-4i + x) = 0 ((195 + -39x) + 10x * (-5 + x) + x2(-5 + x))(-4i + x) = 0 (195 + -39x + (-5 * 10x + x * 10x) + x2(-5 + x))(-4i + x) = 0 (195 + -39x + (-50x + 10x2) + x2(-5 + x))(-4i + x) = 0 (195 + -39x + -50x + 10x2 + (-5 * x2 + x * x2))(-4i + x) = 0 (195 + -39x + -50x + 10x2 + (-5x2 + x3))(-4i + x) = 0 Combine like terms: -39x + -50x = -89x (195 + -89x + 10x2 + -5x2 + x3)(-4i + x) = 0 Combine like terms: 10x2 + -5x2 = 5x2 (195 + -89x + 5x2 + x3)(-4i + x) = 0 Multiply (195 + -89x + 5x2 + x3) * (-4i + x) (195(-4i + x) + -89x * (-4i + x) + 5x2 * (-4i + x) + x3(-4i + x)) = 0 ((-4i * 195 + x * 195) + -89x * (-4i + x) + 5x2 * (-4i + x) + x3(-4i + x)) = 0 ((-780i + 195x) + -89x * (-4i + x) + 5x2 * (-4i + x) + x3(-4i + x)) = 0 (-780i + 195x + (-4i * -89x + x * -89x) + 5x2 * (-4i + x) + x3(-4i + x)) = 0 (-780i + 195x + (356ix + -89x2) + 5x2 * (-4i + x) + x3(-4i + x)) = 0 (-780i + 195x + 356ix + -89x2 + (-4i * 5x2 + x * 5x2) + x3(-4i + x)) = 0 (-780i + 195x + 356ix + -89x2 + (-20ix2 + 5x3) + x3(-4i + x)) = 0 (-780i + 195x + 356ix + -89x2 + -20ix2 + 5x3 + (-4i * x3 + x * x3)) = 0 (-780i + 195x + 356ix + -89x2 + -20ix2 + 5x3 + (-4ix3 + x4)) = 0 Reorder the terms: (-780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4) = 0 (-780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4) = 0 Solving -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-195x' to each side of the equation. -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + -195x + x4 = 0 + -195x Reorder the terms: -780i + 356ix + -20ix2 + -4ix3 + 195x + -195x + -89x2 + 5x3 + x4 = 0 + -195x Combine like terms: 195x + -195x = 0 -780i + 356ix + -20ix2 + -4ix3 + 0 + -89x2 + 5x3 + x4 = 0 + -195x -780i + 356ix + -20ix2 + -4ix3 + -89x2 + 5x3 + x4 = 0 + -195x Remove the zero: -780i + 356ix + -20ix2 + -4ix3 + -89x2 + 5x3 + x4 = -195x Add '89x2' to each side of the equation. -780i + 356ix + -20ix2 + -4ix3 + -89x2 + 5x3 + 89x2 + x4 = -195x + 89x2 Reorder the terms: -780i + 356ix + -20ix2 + -4ix3 + -89x2 + 89x2 + 5x3 + x4 = -195x + 89x2 Combine like terms: -89x2 + 89x2 = 0 -780i + 356ix + -20ix2 + -4ix3 + 0 + 5x3 + x4 = -195x + 89x2 -780i + 356ix + -20ix2 + -4ix3 + 5x3 + x4 = -195x + 89x2 Add '-5x3' to each side of the equation. -780i + 356ix + -20ix2 + -4ix3 + 5x3 + -5x3 + x4 = -195x + 89x2 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -780i + 356ix + -20ix2 + -4ix3 + 0 + x4 = -195x + 89x2 + -5x3 -780i + 356ix + -20ix2 + -4ix3 + x4 = -195x + 89x2 + -5x3 Add '-1x4' to each side of the equation. -780i + 356ix + -20ix2 + -4ix3 + x4 + -1x4 = -195x + 89x2 + -5x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -780i + 356ix + -20ix2 + -4ix3 + 0 = -195x + 89x2 + -5x3 + -1x4 -780i + 356ix + -20ix2 + -4ix3 = -195x + 89x2 + -5x3 + -1x4 Reorder the terms: -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = -195x + 195x + 89x2 + -89x2 + -5x3 + 5x3 + -1x4 + x4 Combine like terms: -195x + 195x = 0 -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = 0 + 89x2 + -89x2 + -5x3 + 5x3 + -1x4 + x4 -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = 89x2 + -89x2 + -5x3 + 5x3 + -1x4 + x4 Combine like terms: 89x2 + -89x2 = 0 -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = 0 + -5x3 + 5x3 + -1x4 + x4 -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = -5x3 + 5x3 + -1x4 + x4 Combine like terms: -5x3 + 5x3 = 0 -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = 0 + -1x4 + x4 -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -780i + 356ix + -20ix2 + -4ix3 + 195x + -89x2 + 5x3 + x4 = 0 The solution to this equation could not be determined.
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