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Simplifying (x + -1(3 + 1))(x + (3 + -1i)) = 0 Combine like terms: 3 + 1 = 4 (x + -1(4))(x + (3 + -1i)) = 0 Multiply -1 * 4 (x + -4)(x + (3 + -1i)) = 0 Reorder the terms: (-4 + x)(x + (3 + -1i)) = 0 Remove parenthesis around (3 + -1i) (-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 = -1x (-12 + 4i + -1ix + -1x + x2) = 0 Solving -12 + 4i + -1ix + -1x + 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 + -1x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 4i + -1ix + -1x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 4i + -1ix + -1x + x2 = 0 + 12 4i + -1ix + -1x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 4i + -1ix + -1x + x2 = 12 Add 'x' to each side of the equation. 4i + -1ix + -1x + x + x2 = 12 + x Combine like terms: -1x + x = 0 4i + -1ix + 0 + x2 = 12 + x 4i + -1ix + x2 = 12 + x Add '-1x2' to each side of the equation. 4i + -1ix + x2 + -1x2 = 12 + x + -1x2 Combine like terms: x2 + -1x2 = 0 4i + -1ix + 0 = 12 + x + -1x2 4i + -1ix = 12 + x + -1x2 Reorder the terms: -12 + 4i + -1ix + -1x + x2 = 12 + x + -1x2 + -12 + -1x + x2 Reorder the terms: -12 + 4i + -1ix + -1x + x2 = 12 + -12 + x + -1x + -1x2 + x2 Combine like terms: 12 + -12 = 0 -12 + 4i + -1ix + -1x + x2 = 0 + x + -1x + -1x2 + x2 -12 + 4i + -1ix + -1x + x2 = x + -1x + -1x2 + x2 Combine like terms: x + -1x = 0 -12 + 4i + -1ix + -1x + x2 = 0 + -1x2 + x2 -12 + 4i + -1ix + -1x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -12 + 4i + -1ix + -1x + x2 = 0 The solution to this equation could not be determined.
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