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Simplifying (x + 4)(x + -1 + i)(x + -1 + -1i) = 0 Reorder the terms: (4 + x)(x + -1 + i)(x + -1 + -1i) = 0 Reorder the terms: (4 + x)(-1 + i + x)(x + -1 + -1i) = 0 Reorder the terms: (4 + x)(-1 + i + x)(-1 + -1i + x) = 0 Multiply (4 + x) * (-1 + i + x) (4(-1 + i + x) + x(-1 + i + x))(-1 + -1i + x) = 0 ((-1 * 4 + i * 4 + x * 4) + x(-1 + i + x))(-1 + -1i + x) = 0 ((-4 + 4i + 4x) + x(-1 + i + x))(-1 + -1i + x) = 0 (-4 + 4i + 4x + (-1 * x + i * x + x * x))(-1 + -1i + x) = 0 Reorder the terms: (-4 + 4i + 4x + (ix + -1x + x2))(-1 + -1i + x) = 0 (-4 + 4i + 4x + (ix + -1x + x2))(-1 + -1i + x) = 0 Reorder the terms: (-4 + 4i + ix + 4x + -1x + x2)(-1 + -1i + x) = 0 Combine like terms: 4x + -1x = 3x (-4 + 4i + ix + 3x + x2)(-1 + -1i + x) = 0 Multiply (-4 + 4i + ix + 3x + x2) * (-1 + -1i + x) (-4(-1 + -1i + x) + 4i * (-1 + -1i + x) + ix(-1 + -1i + x) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 ((-1 * -4 + -1i * -4 + x * -4) + 4i * (-1 + -1i + x) + ix(-1 + -1i + x) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 ((4 + 4i + -4x) + 4i * (-1 + -1i + x) + ix(-1 + -1i + x) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 (4 + 4i + -4x + (-1 * 4i + -1i * 4i + x * 4i) + ix(-1 + -1i + x) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 Reorder the terms: (4 + 4i + -4x + (-4i + 4ix + -4i2) + ix(-1 + -1i + x) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 (4 + 4i + -4x + (-4i + 4ix + -4i2) + ix(-1 + -1i + x) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 (4 + 4i + -4x + -4i + 4ix + -4i2 + (-1 * ix + -1i * ix + x * ix) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 Reorder the terms: (4 + 4i + -4x + -4i + 4ix + -4i2 + (-1ix + ix2 + -1i2x) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 (4 + 4i + -4x + -4i + 4ix + -4i2 + (-1ix + ix2 + -1i2x) + 3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 (4 + 4i + -4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + (-1 * 3x + -1i * 3x + x * 3x) + x2(-1 + -1i + x)) = 0 Reorder the terms: (4 + 4i + -4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + (-3ix + -3x + 3x2) + x2(-1 + -1i + x)) = 0 (4 + 4i + -4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + (-3ix + -3x + 3x2) + x2(-1 + -1i + x)) = 0 (4 + 4i + -4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + -3ix + -3x + 3x2 + (-1 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (4 + 4i + -4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + -3ix + -3x + 3x2 + (-1ix2 + -1x2 + x3)) = 0 (4 + 4i + -4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + -3ix + -3x + 3x2 + (-1ix2 + -1x2 + x3)) = 0 Reorder the terms: (4 + 4i + -4i + 4ix + -1ix + -3ix + ix2 + -1ix2 + -4i2 + -1i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: 4i + -4i = 0 (4 + 0 + 4ix + -1ix + -3ix + ix2 + -1ix2 + -4i2 + -1i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 (4 + 4ix + -1ix + -3ix + ix2 + -1ix2 + -4i2 + -1i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: 4ix + -1ix = 3ix (4 + 3ix + -3ix + ix2 + -1ix2 + -4i2 + -1i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: 3ix + -3ix = 0 (4 + 0 + ix2 + -1ix2 + -4i2 + -1i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 (4 + ix2 + -1ix2 + -4i2 + -1i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (4 + 0 + -4i2 + -1i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 (4 + -4i2 + -1i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: -4x + -3x = -7x (4 + -4i2 + -1i2x + -7x + 3x2 + -1x2 + x3) = 0 Combine like terms: 3x2 + -1x2 = 2x2 (4 + -4i2 + -1i2x + -7x + 2x2 + x3) = 0 Solving 4 + -4i2 + -1i2x + -7x + 2x2 + 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 + -7x + 2x2 + -4 + x3 = 0 + -4 Reorder the terms: 4 + -4 + -4i2 + -1i2x + -7x + 2x2 + x3 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4i2 + -1i2x + -7x + 2x2 + x3 = 0 + -4 -4i2 + -1i2x + -7x + 2x2 + x3 = 0 + -4 Combine like terms: 0 + -4 = -4 -4i2 + -1i2x + -7x + 2x2 + x3 = -4 Add '7x' to each side of the equation. -4i2 + -1i2x + -7x + 2x2 + 7x + x3 = -4 + 7x Reorder the terms: -4i2 + -1i2x + -7x + 7x + 2x2 + x3 = -4 + 7x Combine like terms: -7x + 7x = 0 -4i2 + -1i2x + 0 + 2x2 + x3 = -4 + 7x -4i2 + -1i2x + 2x2 + x3 = -4 + 7x Add '-2x2' to each side of the equation. -4i2 + -1i2x + 2x2 + -2x2 + x3 = -4 + 7x + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4i2 + -1i2x + 0 + x3 = -4 + 7x + -2x2 -4i2 + -1i2x + x3 = -4 + 7x + -2x2 Add '-1x3' to each side of the equation. -4i2 + -1i2x + x3 + -1x3 = -4 + 7x + -2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -4i2 + -1i2x + 0 = -4 + 7x + -2x2 + -1x3 -4i2 + -1i2x = -4 + 7x + -2x2 + -1x3 Reorder the terms: 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = -4 + 7x + -2x2 + -1x3 + 4 + -7x + 2x2 + x3 Reorder the terms: 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = -4 + 4 + 7x + -7x + -2x2 + 2x2 + -1x3 + x3 Combine like terms: -4 + 4 = 0 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = 0 + 7x + -7x + -2x2 + 2x2 + -1x3 + x3 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = 7x + -7x + -2x2 + 2x2 + -1x3 + x3 Combine like terms: 7x + -7x = 0 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = 0 + -2x2 + 2x2 + -1x3 + x3 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = -2x2 + 2x2 + -1x3 + x3 Combine like terms: -2x2 + 2x2 = 0 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = 0 + -1x3 + x3 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 4 + -4i2 + -1i2x + -7x + 2x2 + x3 = 0 The solution to this equation could not be determined.
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