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Simplifying (x + 2)(x + -6i)(x + 6i) = 0 Reorder the terms: (2 + x)(x + -6i)(x + 6i) = 0 Reorder the terms: (2 + x)(-6i + x)(x + 6i) = 0 Reorder the terms: (2 + x)(-6i + x)(6i + x) = 0 Multiply (2 + x) * (-6i + x) (2(-6i + x) + x(-6i + x))(6i + x) = 0 ((-6i * 2 + x * 2) + x(-6i + x))(6i + x) = 0 ((-12i + 2x) + x(-6i + x))(6i + x) = 0 (-12i + 2x + (-6i * x + x * x))(6i + x) = 0 (-12i + 2x + (-6ix + x2))(6i + x) = 0 Reorder the terms: (-12i + -6ix + 2x + x2)(6i + x) = 0 (-12i + -6ix + 2x + x2)(6i + x) = 0 Multiply (-12i + -6ix + 2x + x2) * (6i + x) (-12i * (6i + x) + -6ix * (6i + x) + 2x * (6i + x) + x2(6i + x)) = 0 ((6i * -12i + x * -12i) + -6ix * (6i + x) + 2x * (6i + x) + x2(6i + x)) = 0 Reorder the terms: ((-12ix + -72i2) + -6ix * (6i + x) + 2x * (6i + x) + x2(6i + x)) = 0 ((-12ix + -72i2) + -6ix * (6i + x) + 2x * (6i + x) + x2(6i + x)) = 0 (-12ix + -72i2 + (6i * -6ix + x * -6ix) + 2x * (6i + x) + x2(6i + x)) = 0 Reorder the terms: (-12ix + -72i2 + (-6ix2 + -36i2x) + 2x * (6i + x) + x2(6i + x)) = 0 (-12ix + -72i2 + (-6ix2 + -36i2x) + 2x * (6i + x) + x2(6i + x)) = 0 (-12ix + -72i2 + -6ix2 + -36i2x + (6i * 2x + x * 2x) + x2(6i + x)) = 0 (-12ix + -72i2 + -6ix2 + -36i2x + (12ix + 2x2) + x2(6i + x)) = 0 (-12ix + -72i2 + -6ix2 + -36i2x + 12ix + 2x2 + (6i * x2 + x * x2)) = 0 (-12ix + -72i2 + -6ix2 + -36i2x + 12ix + 2x2 + (6ix2 + x3)) = 0 Reorder the terms: (-12ix + 12ix + -6ix2 + 6ix2 + -72i2 + -36i2x + 2x2 + x3) = 0 Combine like terms: -12ix + 12ix = 0 (0 + -6ix2 + 6ix2 + -72i2 + -36i2x + 2x2 + x3) = 0 (-6ix2 + 6ix2 + -72i2 + -36i2x + 2x2 + x3) = 0 Combine like terms: -6ix2 + 6ix2 = 0 (0 + -72i2 + -36i2x + 2x2 + x3) = 0 (-72i2 + -36i2x + 2x2 + x3) = 0 Solving -72i2 + -36i2x + 2x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2x2' to each side of the equation. -72i2 + -36i2x + 2x2 + -2x2 + x3 = 0 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -72i2 + -36i2x + 0 + x3 = 0 + -2x2 -72i2 + -36i2x + x3 = 0 + -2x2 Remove the zero: -72i2 + -36i2x + x3 = -2x2 Add '-1x3' to each side of the equation. -72i2 + -36i2x + x3 + -1x3 = -2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -72i2 + -36i2x + 0 = -2x2 + -1x3 -72i2 + -36i2x = -2x2 + -1x3 Reorder the terms: -72i2 + -36i2x + 2x2 + x3 = -2x2 + 2x2 + -1x3 + x3 Combine like terms: -2x2 + 2x2 = 0 -72i2 + -36i2x + 2x2 + x3 = 0 + -1x3 + x3 -72i2 + -36i2x + 2x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -72i2 + -36i2x + 2x2 + x3 = 0 The solution to this equation could not be determined.
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