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Simplifying (x + -4)(x + -4)(x + -3i)(x + 3i) = 0 Reorder the terms: (-4 + x)(x + -4)(x + -3i)(x + 3i) = 0 Reorder the terms: (-4 + x)(-4 + x)(x + -3i)(x + 3i) = 0 Reorder the terms: (-4 + x)(-4 + x)(-3i + x)(x + 3i) = 0 Reorder the terms: (-4 + x)(-4 + x)(-3i + x)(3i + x) = 0 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x))(-3i + x)(3i + x) = 0 ((-4 * -4 + x * -4) + x(-4 + x))(-3i + x)(3i + x) = 0 ((16 + -4x) + x(-4 + x))(-3i + x)(3i + x) = 0 (16 + -4x + (-4 * x + x * x))(-3i + x)(3i + x) = 0 (16 + -4x + (-4x + x2))(-3i + x)(3i + x) = 0 Combine like terms: -4x + -4x = -8x (16 + -8x + x2)(-3i + x)(3i + x) = 0 Multiply (16 + -8x + x2) * (-3i + x) (16(-3i + x) + -8x * (-3i + x) + x2(-3i + x))(3i + x) = 0 ((-3i * 16 + x * 16) + -8x * (-3i + x) + x2(-3i + x))(3i + x) = 0 ((-48i + 16x) + -8x * (-3i + x) + x2(-3i + x))(3i + x) = 0 (-48i + 16x + (-3i * -8x + x * -8x) + x2(-3i + x))(3i + x) = 0 (-48i + 16x + (24ix + -8x2) + x2(-3i + x))(3i + x) = 0 (-48i + 16x + 24ix + -8x2 + (-3i * x2 + x * x2))(3i + x) = 0 (-48i + 16x + 24ix + -8x2 + (-3ix2 + x3))(3i + x) = 0 Reorder the terms: (-48i + 24ix + -3ix2 + 16x + -8x2 + x3)(3i + x) = 0 (-48i + 24ix + -3ix2 + 16x + -8x2 + x3)(3i + x) = 0 Multiply (-48i + 24ix + -3ix2 + 16x + -8x2 + x3) * (3i + x) (-48i * (3i + x) + 24ix * (3i + x) + -3ix2 * (3i + x) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 ((3i * -48i + x * -48i) + 24ix * (3i + x) + -3ix2 * (3i + x) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: ((-48ix + -144i2) + 24ix * (3i + x) + -3ix2 * (3i + x) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 ((-48ix + -144i2) + 24ix * (3i + x) + -3ix2 * (3i + x) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 (-48ix + -144i2 + (3i * 24ix + x * 24ix) + -3ix2 * (3i + x) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: (-48ix + -144i2 + (24ix2 + 72i2x) + -3ix2 * (3i + x) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 (-48ix + -144i2 + (24ix2 + 72i2x) + -3ix2 * (3i + x) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 (-48ix + -144i2 + 24ix2 + 72i2x + (3i * -3ix2 + x * -3ix2) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: (-48ix + -144i2 + 24ix2 + 72i2x + (-3ix3 + -9i2x2) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 (-48ix + -144i2 + 24ix2 + 72i2x + (-3ix3 + -9i2x2) + 16x * (3i + x) + -8x2 * (3i + x) + x3(3i + x)) = 0 (-48ix + -144i2 + 24ix2 + 72i2x + -3ix3 + -9i2x2 + (3i * 16x + x * 16x) + -8x2 * (3i + x) + x3(3i + x)) = 0 (-48ix + -144i2 + 24ix2 + 72i2x + -3ix3 + -9i2x2 + (48ix + 16x2) + -8x2 * (3i + x) + x3(3i + x)) = 0 (-48ix + -144i2 + 24ix2 + 72i2x + -3ix3 + -9i2x2 + 48ix + 16x2 + (3i * -8x2 + x * -8x2) + x3(3i + x)) = 0 (-48ix + -144i2 + 24ix2 + 72i2x + -3ix3 + -9i2x2 + 48ix + 16x2 + (-24ix2 + -8x3) + x3(3i + x)) = 0 (-48ix + -144i2 + 24ix2 + 72i2x + -3ix3 + -9i2x2 + 48ix + 16x2 + -24ix2 + -8x3 + (3i * x3 + x * x3)) = 0 (-48ix + -144i2 + 24ix2 + 72i2x + -3ix3 + -9i2x2 + 48ix + 16x2 + -24ix2 + -8x3 + (3ix3 + x4)) = 0 Reorder the terms: (-48ix + 48ix + 24ix2 + -24ix2 + -3ix3 + 3ix3 + -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4) = 0 Combine like terms: -48ix + 48ix = 0 (0 + 24ix2 + -24ix2 + -3ix3 + 3ix3 + -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4) = 0 (24ix2 + -24ix2 + -3ix3 + 3ix3 + -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4) = 0 Combine like terms: 24ix2 + -24ix2 = 0 (0 + -3ix3 + 3ix3 + -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4) = 0 (-3ix3 + 3ix3 + -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4) = 0 Combine like terms: -3ix3 + 3ix3 = 0 (0 + -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4) = 0 (-144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4) = 0 Solving -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16x2' to each side of the equation. -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + -16x2 + x4 = 0 + -16x2 Reorder the terms: -144i2 + 72i2x + -9i2x2 + 16x2 + -16x2 + -8x3 + x4 = 0 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -144i2 + 72i2x + -9i2x2 + 0 + -8x3 + x4 = 0 + -16x2 -144i2 + 72i2x + -9i2x2 + -8x3 + x4 = 0 + -16x2 Remove the zero: -144i2 + 72i2x + -9i2x2 + -8x3 + x4 = -16x2 Add '8x3' to each side of the equation. -144i2 + 72i2x + -9i2x2 + -8x3 + 8x3 + x4 = -16x2 + 8x3 Combine like terms: -8x3 + 8x3 = 0 -144i2 + 72i2x + -9i2x2 + 0 + x4 = -16x2 + 8x3 -144i2 + 72i2x + -9i2x2 + x4 = -16x2 + 8x3 Add '-1x4' to each side of the equation. -144i2 + 72i2x + -9i2x2 + x4 + -1x4 = -16x2 + 8x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -144i2 + 72i2x + -9i2x2 + 0 = -16x2 + 8x3 + -1x4 -144i2 + 72i2x + -9i2x2 = -16x2 + 8x3 + -1x4 Reorder the terms: -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4 = -16x2 + 16x2 + 8x3 + -8x3 + -1x4 + x4 Combine like terms: -16x2 + 16x2 = 0 -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4 = 0 + 8x3 + -8x3 + -1x4 + x4 -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4 = 8x3 + -8x3 + -1x4 + x4 Combine like terms: 8x3 + -8x3 = 0 -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4 = 0 + -1x4 + x4 -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -144i2 + 72i2x + -9i2x2 + 16x2 + -8x3 + x4 = 0 The solution to this equation could not be determined.
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