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Simplifying [(x + -1(1 + 2i))(x + -1(x + -2i))](x + -1(-4)) = 0 [(x + (1 * -1 + 2i * -1))(x + -1(x + -2i))](x + -1(-4)) = 0 [(x + (-1 + -2i))(x + -1(x + -2i))](x + -1(-4)) = 0 Reorder the terms: [(-1 + -2i + x)(x + -1(x + -2i))](x + -1(-4)) = 0 Reorder the terms: [(-1 + -2i + x)(x + -1(-2i + x))](x + -1(-4)) = 0 [(-1 + -2i + x)(x + (-2i * -1 + x * -1))](x + -1(-4)) = 0 [(-1 + -2i + x)(x + (2i + -1x))](x + -1(-4)) = 0 Reorder the terms: [(-1 + -2i + x)(2i + x + -1x)](x + -1(-4)) = 0 Combine like terms: x + -1x = 0 [(-1 + -2i + x)(2i + 0)](x + -1(-4)) = 0 [(-1 + -2i + x)(2i)](x + -1(-4)) = 0 Remove parenthesis around (2i) [(-1 + -2i + x) * 2i](x + -1(-4)) = 0 Reorder the terms for easier multiplication: [2i(-1 + -2i + x)](x + -1(-4)) = 0 [(-1 * 2i + -2i * 2i + x * 2i)](x + -1(-4)) = 0 Reorder the terms: [(-2i + 2ix + -4i2)](x + -1(-4)) = 0 [(-2i + 2ix + -4i2)](x + -1(-4)) = 0 Multiply -1 * -4 [-2i + 2ix + -4i2](x + 4) = 0 Reorder the terms: [-2i + 2ix + -4i2](4 + x) = 0 Multiply [-2i + 2ix + -4i2] * (4 + x) [-2i * (4 + x) + 2ix * (4 + x) + -4i2 * (4 + x)] = 0 [(4 * -2i + x * -2i) + 2ix * (4 + x) + -4i2 * (4 + x)] = 0 [(-8i + -2ix) + 2ix * (4 + x) + -4i2 * (4 + x)] = 0 [-8i + -2ix + (4 * 2ix + x * 2ix) + -4i2 * (4 + x)] = 0 [-8i + -2ix + (8ix + 2ix2) + -4i2 * (4 + x)] = 0 [-8i + -2ix + 8ix + 2ix2 + (4 * -4i2 + x * -4i2)] = 0 [-8i + -2ix + 8ix + 2ix2 + (-16i2 + -4i2x)] = 0 Combine like terms: -2ix + 8ix = 6ix [-8i + 6ix + 2ix2 + -16i2 + -4i2x] = 0 Solving -8i + 6ix + 2ix2 + -16i2 + -4i2x = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2i'. 2i(-4 + 3x + x2 + -8i + -2ix) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(-4 + 3x + x2 + -8i + -2ix)' equal to zero and attempt to solve: Simplifying -4 + 3x + x2 + -8i + -2ix = 0 Reorder the terms: -4 + -8i + -2ix + 3x + x2 = 0 Solving -4 + -8i + -2ix + 3x + x2 = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + -8i + -2ix + 3x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -8i + -2ix + 3x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8i + -2ix + 3x + x2 = 0 + 4 -8i + -2ix + 3x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8i + -2ix + 3x + x2 = 4 Add '-3x' to each side of the equation. -8i + -2ix + 3x + -3x + x2 = 4 + -3x Combine like terms: 3x + -3x = 0 -8i + -2ix + 0 + x2 = 4 + -3x -8i + -2ix + x2 = 4 + -3x Add '-1x2' to each side of the equation. -8i + -2ix + x2 + -1x2 = 4 + -3x + -1x2 Combine like terms: x2 + -1x2 = 0 -8i + -2ix + 0 = 4 + -3x + -1x2 -8i + -2ix = 4 + -3x + -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
i = {0}
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