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Simplifying (x + -1)(x + 2)(x + 2i) = 0 Reorder the terms: (-1 + x)(x + 2)(x + 2i) = 0 Reorder the terms: (-1 + x)(2 + x)(x + 2i) = 0 Reorder the terms: (-1 + x)(2 + x)(2i + x) = 0 Multiply (-1 + x) * (2 + x) (-1(2 + x) + x(2 + x))(2i + x) = 0 ((2 * -1 + x * -1) + x(2 + x))(2i + x) = 0 ((-2 + -1x) + x(2 + x))(2i + x) = 0 (-2 + -1x + (2 * x + x * x))(2i + x) = 0 (-2 + -1x + (2x + x2))(2i + x) = 0 Combine like terms: -1x + 2x = 1x (-2 + 1x + x2)(2i + x) = 0 Multiply (-2 + 1x + x2) * (2i + x) (-2(2i + x) + 1x * (2i + x) + x2(2i + x)) = 0 ((2i * -2 + x * -2) + 1x * (2i + x) + x2(2i + x)) = 0 ((-4i + -2x) + 1x * (2i + x) + x2(2i + x)) = 0 (-4i + -2x + (2i * 1x + x * 1x) + x2(2i + x)) = 0 (-4i + -2x + (2ix + 1x2) + x2(2i + x)) = 0 (-4i + -2x + 2ix + 1x2 + (2i * x2 + x * x2)) = 0 (-4i + -2x + 2ix + 1x2 + (2ix2 + x3)) = 0 Reorder the terms: (-4i + 2ix + 2ix2 + -2x + 1x2 + x3) = 0 (-4i + 2ix + 2ix2 + -2x + 1x2 + x3) = 0 Solving -4i + 2ix + 2ix2 + -2x + 1x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2x' to each side of the equation. -4i + 2ix + 2ix2 + -2x + 1x2 + 2x + x3 = 0 + 2x Reorder the terms: -4i + 2ix + 2ix2 + -2x + 2x + 1x2 + x3 = 0 + 2x Combine like terms: -2x + 2x = 0 -4i + 2ix + 2ix2 + 0 + 1x2 + x3 = 0 + 2x -4i + 2ix + 2ix2 + 1x2 + x3 = 0 + 2x Remove the zero: -4i + 2ix + 2ix2 + 1x2 + x3 = 2x Add '-1x2' to each side of the equation. -4i + 2ix + 2ix2 + 1x2 + -1x2 + x3 = 2x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -4i + 2ix + 2ix2 + 0 + x3 = 2x + -1x2 -4i + 2ix + 2ix2 + x3 = 2x + -1x2 Add '-1x3' to each side of the equation. -4i + 2ix + 2ix2 + x3 + -1x3 = 2x + -1x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -4i + 2ix + 2ix2 + 0 = 2x + -1x2 + -1x3 -4i + 2ix + 2ix2 = 2x + -1x2 + -1x3 Reorder the terms: -4i + 2ix + 2ix2 + -2x + x2 + x3 = 2x + -2x + -1x2 + x2 + -1x3 + x3 Combine like terms: 2x + -2x = 0 -4i + 2ix + 2ix2 + -2x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3 -4i + 2ix + 2ix2 + -2x + x2 + x3 = -1x2 + x2 + -1x3 + x3 Combine like terms: -1x2 + x2 = 0 -4i + 2ix + 2ix2 + -2x + x2 + x3 = 0 + -1x3 + x3 -4i + 2ix + 2ix2 + -2x + x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -4i + 2ix + 2ix2 + -2x + x2 + x3 = 0 The solution to this equation could not be determined.
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