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Simplifying (x + -1(3 + -1i))(x + -1(3 + 1)) = 0 (x + (3 * -1 + -1i * -1))(x + -1(3 + 1)) = 0 (x + (-3 + 1i))(x + -1(3 + 1)) = 0 Reorder the terms: (-3 + 1i + x)(x + -1(3 + 1)) = 0 Combine like terms: 3 + 1 = 4 (-3 + 1i + x)(x + -1(4)) = 0 Multiply -1 * 4 (-3 + 1i + x)(x + -4) = 0 Reorder the terms: (-3 + 1i + x)(-4 + x) = 0 Multiply (-3 + 1i + x) * (-4 + x) (-3(-4 + x) + 1i * (-4 + x) + x(-4 + x)) = 0 ((-4 * -3 + x * -3) + 1i * (-4 + x) + x(-4 + x)) = 0 ((12 + -3x) + 1i * (-4 + x) + x(-4 + x)) = 0 (12 + -3x + (-4 * 1i + x * 1i) + x(-4 + x)) = 0 (12 + -3x + (-4i + 1ix) + x(-4 + x)) = 0 (12 + -3x + -4i + 1ix + (-4 * x + x * x)) = 0 (12 + -3x + -4i + 1ix + (-4x + x2)) = 0 Reorder the terms: (12 + -4i + 1ix + -3x + -4x + x2) = 0 Combine like terms: -3x + -4x = -7x (12 + -4i + 1ix + -7x + x2) = 0 Solving 12 + -4i + 1ix + -7x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -4i + 1ix + -7x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -4i + 1ix + -7x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -4i + 1ix + -7x + x2 = 0 + -12 -4i + 1ix + -7x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -4i + 1ix + -7x + x2 = -12 Add '7x' to each side of the equation. -4i + 1ix + -7x + 7x + x2 = -12 + 7x Combine like terms: -7x + 7x = 0 -4i + 1ix + 0 + x2 = -12 + 7x -4i + 1ix + x2 = -12 + 7x Add '-1x2' to each side of the equation. -4i + 1ix + x2 + -1x2 = -12 + 7x + -1x2 Combine like terms: x2 + -1x2 = 0 -4i + 1ix + 0 = -12 + 7x + -1x2 -4i + 1ix = -12 + 7x + -1x2 Reorder the terms: 12 + -4i + 1ix + -7x + x2 = -12 + 7x + -1x2 + 12 + -7x + x2 Reorder the terms: 12 + -4i + 1ix + -7x + x2 = -12 + 12 + 7x + -7x + -1x2 + x2 Combine like terms: -12 + 12 = 0 12 + -4i + 1ix + -7x + x2 = 0 + 7x + -7x + -1x2 + x2 12 + -4i + 1ix + -7x + x2 = 7x + -7x + -1x2 + x2 Combine like terms: 7x + -7x = 0 12 + -4i + 1ix + -7x + x2 = 0 + -1x2 + x2 12 + -4i + 1ix + -7x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 12 + -4i + 1ix + -7x + x2 = 0 The solution to this equation could not be determined.
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