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Simplifying (X + 0)(x + -1)(x + -2 + -1i)(x + -2 + i) = 0 Reorder the terms: (0 + X)(x + -1)(x + -2 + -1i)(x + -2 + i) = 0 Remove the zero: (X)(x + -1)(x + -2 + -1i)(x + -2 + i) = 0 Reorder the terms: X(-1 + x)(x + -2 + -1i)(x + -2 + i) = 0 Reorder the terms: X(-1 + x)(-2 + -1i + x)(x + -2 + i) = 0 Reorder the terms: X(-1 + x)(-2 + -1i + x)(-2 + i + x) = 0 Multiply (-1 + x) * (-2 + -1i + x) X(-1(-2 + -1i + x) + x(-2 + -1i + x))(-2 + i + x) = 0 X((-2 * -1 + -1i * -1 + x * -1) + x(-2 + -1i + x))(-2 + i + x) = 0 X((2 + 1i + -1x) + x(-2 + -1i + x))(-2 + i + x) = 0 X(2 + 1i + -1x + (-2 * x + -1i * x + x * x))(-2 + i + x) = 0 Reorder the terms: X(2 + 1i + -1x + (-1ix + -2x + x2))(-2 + i + x) = 0 X(2 + 1i + -1x + (-1ix + -2x + x2))(-2 + i + x) = 0 Reorder the terms: X(2 + 1i + -1ix + -1x + -2x + x2)(-2 + i + x) = 0 Combine like terms: -1x + -2x = -3x X(2 + 1i + -1ix + -3x + x2)(-2 + i + x) = 0 Multiply (2 + 1i + -1ix + -3x + x2) * (-2 + i + x) X(2(-2 + i + x) + 1i * (-2 + i + x) + -1ix * (-2 + i + x) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 X((-2 * 2 + i * 2 + x * 2) + 1i * (-2 + i + x) + -1ix * (-2 + i + x) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 X((-4 + 2i + 2x) + 1i * (-2 + i + x) + -1ix * (-2 + i + x) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 X(-4 + 2i + 2x + (-2 * 1i + i * 1i + x * 1i) + -1ix * (-2 + i + x) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 Reorder the terms: X(-4 + 2i + 2x + (-2i + 1ix + 1i2) + -1ix * (-2 + i + x) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 X(-4 + 2i + 2x + (-2i + 1ix + 1i2) + -1ix * (-2 + i + x) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 X(-4 + 2i + 2x + -2i + 1ix + 1i2 + (-2 * -1ix + i * -1ix + x * -1ix) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 Reorder the terms: X(-4 + 2i + 2x + -2i + 1ix + 1i2 + (2ix + -1ix2 + -1i2x) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 X(-4 + 2i + 2x + -2i + 1ix + 1i2 + (2ix + -1ix2 + -1i2x) + -3x * (-2 + i + x) + x2(-2 + i + x)) = 0 X(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-2 * -3x + i * -3x + x * -3x) + x2(-2 + i + x)) = 0 Reorder the terms: X(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-3ix + 6x + -3x2) + x2(-2 + i + x)) = 0 X(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-3ix + 6x + -3x2) + x2(-2 + i + x)) = 0 X(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (-2 * x2 + i * x2 + x * x2)) = 0 Reorder the terms: X(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (ix2 + -2x2 + x3)) = 0 X(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (ix2 + -2x2 + x3)) = 0 Reorder the terms: X(-4 + 2i + -2i + 1ix + 2ix + -3ix + -1ix2 + ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: 2i + -2i = 0 X(-4 + 0 + 1ix + 2ix + -3ix + -1ix2 + ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 X(-4 + 1ix + 2ix + -3ix + -1ix2 + ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: 1ix + 2ix = 3ix X(-4 + 3ix + -3ix + -1ix2 + ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: 3ix + -3ix = 0 X(-4 + 0 + -1ix2 + ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 X(-4 + -1ix2 + ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: -1ix2 + ix2 = 0 X(-4 + 0 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 X(-4 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0 Combine like terms: 2x + 6x = 8x X(-4 + 1i2 + -1i2x + 8x + -3x2 + -2x2 + x3) = 0 Combine like terms: -3x2 + -2x2 = -5x2 X(-4 + 1i2 + -1i2x + 8x + -5x2 + x3) = 0 (-4 * X + 1i2 * X + -1i2x * X + 8x * X + -5x2 * X + x3 * X) = 0 (-4X + 1i2X + -1i2xX + 8xX + -5x2X + x3X) = 0 Solving -4X + 1i2X + -1i2xX + 8xX + -5x2X + x3X = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'X'. X(-4 + i2 + -1i2x + 8x + -5x2 + x3) = 0Subproblem 1
Set the factor 'X' equal to zero and attempt to solve: Simplifying X = 0 Solving X = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X = 0Subproblem 2
Set the factor '(-4 + i2 + -1i2x + 8x + -5x2 + x3)' equal to zero and attempt to solve: Simplifying -4 + i2 + -1i2x + 8x + -5x2 + x3 = 0 Solving -4 + i2 + -1i2x + 8x + -5x2 + x3 = 0 Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + i2 + -1i2x + 8x + -5x2 + 4 + x3 = 0 + 4 Reorder the terms: -4 + 4 + i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4 i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4 Combine like terms: 0 + 4 = 4 i2 + -1i2x + 8x + -5x2 + x3 = 4 Add '-1i2' to each side of the equation. i2 + -1i2x + 8x + -5x2 + -1i2 + x3 = 4 + -1i2 Reorder the terms: i2 + -1i2 + -1i2x + 8x + -5x2 + x3 = 4 + -1i2 Combine like terms: i2 + -1i2 = 0 0 + -1i2x + 8x + -5x2 + x3 = 4 + -1i2 -1i2x + 8x + -5x2 + x3 = 4 + -1i2 Add 'i2x' to each side of the equation. -1i2x + 8x + -5x2 + i2x + x3 = 4 + -1i2 + i2x Reorder the terms: -1i2x + i2x + 8x + -5x2 + x3 = 4 + -1i2 + i2x Combine like terms: -1i2x + i2x = 0 0 + 8x + -5x2 + x3 = 4 + -1i2 + i2x 8x + -5x2 + x3 = 4 + -1i2 + i2x Add '-8x' to each side of the equation. 8x + -5x2 + -8x + x3 = 4 + -1i2 + i2x + -8x Reorder the terms: 8x + -8x + -5x2 + x3 = 4 + -1i2 + i2x + -8x Combine like terms: 8x + -8x = 0 0 + -5x2 + x3 = 4 + -1i2 + i2x + -8x -5x2 + x3 = 4 + -1i2 + i2x + -8x Add '5x2' to each side of the equation. -5x2 + 5x2 + x3 = 4 + -1i2 + i2x + -8x + 5x2 Combine like terms: -5x2 + 5x2 = 0 0 + x3 = 4 + -1i2 + i2x + -8x + 5x2 x3 = 4 + -1i2 + i2x + -8x + 5x2 Add '-1x3' to each side of the equation. x3 + -1x3 = 4 + -1i2 + i2x + -8x + 5x2 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = 4 + -1i2 + i2x + -8x + 5x2 + -1x3 Simplifying 0 = 4 + -1i2 + i2x + -8x + 5x2 + -1x3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
X = {0}
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