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Simplifying (x + -1(3 + 1))(x + -1(3 + -1i)) = 0 Combine like terms: 3 + 1 = 4 (x + -1(4))(x + -1(3 + -1i)) = 0 Multiply -1 * 4 (x + -4)(x + -1(3 + -1i)) = 0 Reorder the terms: (-4 + x)(x + -1(3 + -1i)) = 0 (-4 + x)(x + (3 * -1 + -1i * -1)) = 0 (-4 + x)(x + (-3 + 1i)) = 0 Reorder the terms: (-4 + x)(-3 + 1i + x) = 0 Multiply (-4 + x) * (-3 + 1i + x) (-4(-3 + 1i + x) + x(-3 + 1i + x)) = 0 ((-3 * -4 + 1i * -4 + x * -4) + x(-3 + 1i + x)) = 0 ((12 + -4i + -4x) + x(-3 + 1i + x)) = 0 (12 + -4i + -4x + (-3 * x + 1i * x + x * x)) = 0 Reorder the terms: (12 + -4i + -4x + (1ix + -3x + x2)) = 0 (12 + -4i + -4x + (1ix + -3x + x2)) = 0 Reorder the terms: (12 + -4i + 1ix + -4x + -3x + x2) = 0 Combine like terms: -4x + -3x = -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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