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Simplifying (x + -4)(x + -1 + -1i)(x + -1 + i) = 0 Reorder the terms: (-4 + x)(x + -1 + -1i)(x + -1 + i) = 0 Reorder the terms: (-4 + x)(-1 + -1i + x)(x + -1 + i) = 0 Reorder the terms: (-4 + x)(-1 + -1i + x)(-1 + i + x) = 0 Multiply (-4 + x) * (-1 + -1i + x) (-4(-1 + -1i + x) + x(-1 + -1i + x))(-1 + i + x) = 0 ((-1 * -4 + -1i * -4 + x * -4) + x(-1 + -1i + x))(-1 + i + x) = 0 ((4 + 4i + -4x) + x(-1 + -1i + x))(-1 + i + x) = 0 (4 + 4i + -4x + (-1 * x + -1i * x + x * x))(-1 + i + x) = 0 Reorder the terms: (4 + 4i + -4x + (-1ix + -1x + x2))(-1 + i + x) = 0 (4 + 4i + -4x + (-1ix + -1x + x2))(-1 + i + x) = 0 Reorder the terms: (4 + 4i + -1ix + -4x + -1x + x2)(-1 + i + x) = 0 Combine like terms: -4x + -1x = -5x (4 + 4i + -1ix + -5x + x2)(-1 + i + x) = 0 Multiply (4 + 4i + -1ix + -5x + x2) * (-1 + i + x) (4(-1 + i + x) + 4i * (-1 + i + x) + -1ix * (-1 + i + x) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 ((-1 * 4 + i * 4 + x * 4) + 4i * (-1 + i + x) + -1ix * (-1 + i + x) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 ((-4 + 4i + 4x) + 4i * (-1 + i + x) + -1ix * (-1 + i + x) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-4 + 4i + 4x + (-1 * 4i + i * 4i + x * 4i) + -1ix * (-1 + i + x) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 Reorder the terms: (-4 + 4i + 4x + (-4i + 4ix + 4i2) + -1ix * (-1 + i + x) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-4 + 4i + 4x + (-4i + 4ix + 4i2) + -1ix * (-1 + i + x) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-4 + 4i + 4x + -4i + 4ix + 4i2 + (-1 * -1ix + i * -1ix + x * -1ix) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 Reorder the terms: (-4 + 4i + 4x + -4i + 4ix + 4i2 + (1ix + -1ix2 + -1i2x) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-4 + 4i + 4x + -4i + 4ix + 4i2 + (1ix + -1ix2 + -1i2x) + -5x * (-1 + i + x) + x2(-1 + i + x)) = 0 (-4 + 4i + 4x + -4i + 4ix + 4i2 + 1ix + -1ix2 + -1i2x + (-1 * -5x + i * -5x + x * -5x) + x2(-1 + i + x)) = 0 Reorder the terms: (-4 + 4i + 4x + -4i + 4ix + 4i2 + 1ix + -1ix2 + -1i2x + (-5ix + 5x + -5x2) + x2(-1 + i + x)) = 0 (-4 + 4i + 4x + -4i + 4ix + 4i2 + 1ix + -1ix2 + -1i2x + (-5ix + 5x + -5x2) + x2(-1 + i + x)) = 0 (-4 + 4i + 4x + -4i + 4ix + 4i2 + 1ix + -1ix2 + -1i2x + -5ix + 5x + -5x2 + (-1 * x2 + i * x2 + x * x2)) = 0 Reorder the terms: (-4 + 4i + 4x + -4i + 4ix + 4i2 + 1ix + -1ix2 + -1i2x + -5ix + 5x + -5x2 + (ix2 + -1x2 + x3)) = 0 (-4 + 4i + 4x + -4i + 4ix + 4i2 + 1ix + -1ix2 + -1i2x + -5ix + 5x + -5x2 + (ix2 + -1x2 + x3)) = 0 Reorder the terms: (-4 + 4i + -4i + 4ix + 1ix + -5ix + -1ix2 + ix2 + 4i2 + -1i2x + 4x + 5x + -5x2 + -1x2 + x3) = 0 Combine like terms: 4i + -4i = 0 (-4 + 0 + 4ix + 1ix + -5ix + -1ix2 + ix2 + 4i2 + -1i2x + 4x + 5x + -5x2 + -1x2 + x3) = 0 (-4 + 4ix + 1ix + -5ix + -1ix2 + ix2 + 4i2 + -1i2x + 4x + 5x + -5x2 + -1x2 + x3) = 0 Combine like terms: 4ix + 1ix = 5ix (-4 + 5ix + -5ix + -1ix2 + ix2 + 4i2 + -1i2x + 4x + 5x + -5x2 + -1x2 + x3) = 0 Combine like terms: 5ix + -5ix = 0 (-4 + 0 + -1ix2 + ix2 + 4i2 + -1i2x + 4x + 5x + -5x2 + -1x2 + x3) = 0 (-4 + -1ix2 + ix2 + 4i2 + -1i2x + 4x + 5x + -5x2 + -1x2 + x3) = 0 Combine like terms: -1ix2 + ix2 = 0 (-4 + 0 + 4i2 + -1i2x + 4x + 5x + -5x2 + -1x2 + x3) = 0 (-4 + 4i2 + -1i2x + 4x + 5x + -5x2 + -1x2 + x3) = 0 Combine like terms: 4x + 5x = 9x (-4 + 4i2 + -1i2x + 9x + -5x2 + -1x2 + x3) = 0 Combine like terms: -5x2 + -1x2 = -6x2 (-4 + 4i2 + -1i2x + 9x + -6x2 + x3) = 0 Solving -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4i2 + -1i2x + 9x + -6x2 + 4 + x3 = 0 + 4 Reorder the terms: -4 + 4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + 4 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + 4 Combine like terms: 0 + 4 = 4 4i2 + -1i2x + 9x + -6x2 + x3 = 4 Add '-9x' to each side of the equation. 4i2 + -1i2x + 9x + -6x2 + -9x + x3 = 4 + -9x Reorder the terms: 4i2 + -1i2x + 9x + -9x + -6x2 + x3 = 4 + -9x Combine like terms: 9x + -9x = 0 4i2 + -1i2x + 0 + -6x2 + x3 = 4 + -9x 4i2 + -1i2x + -6x2 + x3 = 4 + -9x Add '6x2' to each side of the equation. 4i2 + -1i2x + -6x2 + 6x2 + x3 = 4 + -9x + 6x2 Combine like terms: -6x2 + 6x2 = 0 4i2 + -1i2x + 0 + x3 = 4 + -9x + 6x2 4i2 + -1i2x + x3 = 4 + -9x + 6x2 Add '-1x3' to each side of the equation. 4i2 + -1i2x + x3 + -1x3 = 4 + -9x + 6x2 + -1x3 Combine like terms: x3 + -1x3 = 0 4i2 + -1i2x + 0 = 4 + -9x + 6x2 + -1x3 4i2 + -1i2x = 4 + -9x + 6x2 + -1x3 Reorder the terms: -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 4 + -9x + 6x2 + -1x3 + -4 + 9x + -6x2 + x3 Reorder the terms: -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 4 + -4 + -9x + 9x + 6x2 + -6x2 + -1x3 + x3 Combine like terms: 4 + -4 = 0 -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + -9x + 9x + 6x2 + -6x2 + -1x3 + x3 -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = -9x + 9x + 6x2 + -6x2 + -1x3 + x3 Combine like terms: -9x + 9x = 0 -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + 6x2 + -6x2 + -1x3 + x3 -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 6x2 + -6x2 + -1x3 + x3 Combine like terms: 6x2 + -6x2 = 0 -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + -1x3 + x3 -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 The solution to this equation could not be determined.
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