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Simplifying (x + -4 + 3i)(x + -4 + -3i)(x + -3)(x + -3) = 0 Reorder the terms: (-4 + 3i + x)(x + -4 + -3i)(x + -3)(x + -3) = 0 Reorder the terms: (-4 + 3i + x)(-4 + -3i + x)(x + -3)(x + -3) = 0 Reorder the terms: (-4 + 3i + x)(-4 + -3i + x)(-3 + x)(x + -3) = 0 Reorder the terms: (-4 + 3i + x)(-4 + -3i + x)(-3 + x)(-3 + x) = 0 Multiply (-4 + 3i + x) * (-4 + -3i + x) (-4(-4 + -3i + x) + 3i * (-4 + -3i + x) + x(-4 + -3i + x))(-3 + x)(-3 + x) = 0 ((-4 * -4 + -3i * -4 + x * -4) + 3i * (-4 + -3i + x) + x(-4 + -3i + x))(-3 + x)(-3 + x) = 0 ((16 + 12i + -4x) + 3i * (-4 + -3i + x) + x(-4 + -3i + x))(-3 + x)(-3 + x) = 0 (16 + 12i + -4x + (-4 * 3i + -3i * 3i + x * 3i) + x(-4 + -3i + x))(-3 + x)(-3 + x) = 0 Reorder the terms: (16 + 12i + -4x + (-12i + 3ix + -9i2) + x(-4 + -3i + x))(-3 + x)(-3 + x) = 0 (16 + 12i + -4x + (-12i + 3ix + -9i2) + x(-4 + -3i + x))(-3 + x)(-3 + x) = 0 (16 + 12i + -4x + -12i + 3ix + -9i2 + (-4 * x + -3i * x + x * x))(-3 + x)(-3 + x) = 0 Reorder the terms: (16 + 12i + -4x + -12i + 3ix + -9i2 + (-3ix + -4x + x2))(-3 + x)(-3 + x) = 0 (16 + 12i + -4x + -12i + 3ix + -9i2 + (-3ix + -4x + x2))(-3 + x)(-3 + x) = 0 Reorder the terms: (16 + 12i + -12i + 3ix + -3ix + -9i2 + -4x + -4x + x2)(-3 + x)(-3 + x) = 0 Combine like terms: 12i + -12i = 0 (16 + 0 + 3ix + -3ix + -9i2 + -4x + -4x + x2)(-3 + x)(-3 + x) = 0 (16 + 3ix + -3ix + -9i2 + -4x + -4x + x2)(-3 + x)(-3 + x) = 0 Combine like terms: 3ix + -3ix = 0 (16 + 0 + -9i2 + -4x + -4x + x2)(-3 + x)(-3 + x) = 0 (16 + -9i2 + -4x + -4x + x2)(-3 + x)(-3 + x) = 0 Combine like terms: -4x + -4x = -8x (16 + -9i2 + -8x + x2)(-3 + x)(-3 + x) = 0 Multiply (16 + -9i2 + -8x + x2) * (-3 + x) (16(-3 + x) + -9i2 * (-3 + x) + -8x * (-3 + x) + x2(-3 + x))(-3 + x) = 0 ((-3 * 16 + x * 16) + -9i2 * (-3 + x) + -8x * (-3 + x) + x2(-3 + x))(-3 + x) = 0 ((-48 + 16x) + -9i2 * (-3 + x) + -8x * (-3 + x) + x2(-3 + x))(-3 + x) = 0 (-48 + 16x + (-3 * -9i2 + x * -9i2) + -8x * (-3 + x) + x2(-3 + x))(-3 + x) = 0 (-48 + 16x + (27i2 + -9i2x) + -8x * (-3 + x) + x2(-3 + x))(-3 + x) = 0 (-48 + 16x + 27i2 + -9i2x + (-3 * -8x + x * -8x) + x2(-3 + x))(-3 + x) = 0 (-48 + 16x + 27i2 + -9i2x + (24x + -8x2) + x2(-3 + x))(-3 + x) = 0 (-48 + 16x + 27i2 + -9i2x + 24x + -8x2 + (-3 * x2 + x * x2))(-3 + x) = 0 (-48 + 16x + 27i2 + -9i2x + 24x + -8x2 + (-3x2 + x3))(-3 + x) = 0 Reorder the terms: (-48 + 27i2 + -9i2x + 16x + 24x + -8x2 + -3x2 + x3)(-3 + x) = 0 Combine like terms: 16x + 24x = 40x (-48 + 27i2 + -9i2x + 40x + -8x2 + -3x2 + x3)(-3 + x) = 0 Combine like terms: -8x2 + -3x2 = -11x2 (-48 + 27i2 + -9i2x + 40x + -11x2 + x3)(-3 + x) = 0 Multiply (-48 + 27i2 + -9i2x + 40x + -11x2 + x3) * (-3 + x) (-48(-3 + x) + 27i2 * (-3 + x) + -9i2x * (-3 + x) + 40x * (-3 + x) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 ((-3 * -48 + x * -48) + 27i2 * (-3 + x) + -9i2x * (-3 + x) + 40x * (-3 + x) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 ((144 + -48x) + 27i2 * (-3 + x) + -9i2x * (-3 + x) + 40x * (-3 + x) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 (144 + -48x + (-3 * 27i2 + x * 27i2) + -9i2x * (-3 + x) + 40x * (-3 + x) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 (144 + -48x + (-81i2 + 27i2x) + -9i2x * (-3 + x) + 40x * (-3 + x) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 (144 + -48x + -81i2 + 27i2x + (-3 * -9i2x + x * -9i2x) + 40x * (-3 + x) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 (144 + -48x + -81i2 + 27i2x + (27i2x + -9i2x2) + 40x * (-3 + x) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 (144 + -48x + -81i2 + 27i2x + 27i2x + -9i2x2 + (-3 * 40x + x * 40x) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 (144 + -48x + -81i2 + 27i2x + 27i2x + -9i2x2 + (-120x + 40x2) + -11x2 * (-3 + x) + x3(-3 + x)) = 0 (144 + -48x + -81i2 + 27i2x + 27i2x + -9i2x2 + -120x + 40x2 + (-3 * -11x2 + x * -11x2) + x3(-3 + x)) = 0 (144 + -48x + -81i2 + 27i2x + 27i2x + -9i2x2 + -120x + 40x2 + (33x2 + -11x3) + x3(-3 + x)) = 0 (144 + -48x + -81i2 + 27i2x + 27i2x + -9i2x2 + -120x + 40x2 + 33x2 + -11x3 + (-3 * x3 + x * x3)) = 0 (144 + -48x + -81i2 + 27i2x + 27i2x + -9i2x2 + -120x + 40x2 + 33x2 + -11x3 + (-3x3 + x4)) = 0 Reorder the terms: (144 + -81i2 + 27i2x + 27i2x + -9i2x2 + -48x + -120x + 40x2 + 33x2 + -11x3 + -3x3 + x4) = 0 Combine like terms: 27i2x + 27i2x = 54i2x (144 + -81i2 + 54i2x + -9i2x2 + -48x + -120x + 40x2 + 33x2 + -11x3 + -3x3 + x4) = 0 Combine like terms: -48x + -120x = -168x (144 + -81i2 + 54i2x + -9i2x2 + -168x + 40x2 + 33x2 + -11x3 + -3x3 + x4) = 0 Combine like terms: 40x2 + 33x2 = 73x2 (144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -11x3 + -3x3 + x4) = 0 Combine like terms: -11x3 + -3x3 = -14x3 (144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4) = 0 Solving 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-144' to each side of the equation. 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + -144 + x4 = 0 + -144 Reorder the terms: 144 + -144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -144 -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -144 Combine like terms: 0 + -144 = -144 -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = -144 Add '168x' to each side of the equation. -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + 168x + x4 = -144 + 168x Reorder the terms: -81i2 + 54i2x + -9i2x2 + -168x + 168x + 73x2 + -14x3 + x4 = -144 + 168x Combine like terms: -168x + 168x = 0 -81i2 + 54i2x + -9i2x2 + 0 + 73x2 + -14x3 + x4 = -144 + 168x -81i2 + 54i2x + -9i2x2 + 73x2 + -14x3 + x4 = -144 + 168x Add '-73x2' to each side of the equation. -81i2 + 54i2x + -9i2x2 + 73x2 + -14x3 + -73x2 + x4 = -144 + 168x + -73x2 Reorder the terms: -81i2 + 54i2x + -9i2x2 + 73x2 + -73x2 + -14x3 + x4 = -144 + 168x + -73x2 Combine like terms: 73x2 + -73x2 = 0 -81i2 + 54i2x + -9i2x2 + 0 + -14x3 + x4 = -144 + 168x + -73x2 -81i2 + 54i2x + -9i2x2 + -14x3 + x4 = -144 + 168x + -73x2 Add '14x3' to each side of the equation. -81i2 + 54i2x + -9i2x2 + -14x3 + 14x3 + x4 = -144 + 168x + -73x2 + 14x3 Combine like terms: -14x3 + 14x3 = 0 -81i2 + 54i2x + -9i2x2 + 0 + x4 = -144 + 168x + -73x2 + 14x3 -81i2 + 54i2x + -9i2x2 + x4 = -144 + 168x + -73x2 + 14x3 Add '-1x4' to each side of the equation. -81i2 + 54i2x + -9i2x2 + x4 + -1x4 = -144 + 168x + -73x2 + 14x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -81i2 + 54i2x + -9i2x2 + 0 = -144 + 168x + -73x2 + 14x3 + -1x4 -81i2 + 54i2x + -9i2x2 = -144 + 168x + -73x2 + 14x3 + -1x4 Reorder the terms: 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = -144 + 168x + -73x2 + 14x3 + -1x4 + 144 + -168x + 73x2 + -14x3 + x4 Reorder the terms: 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = -144 + 144 + 168x + -168x + -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 Combine like terms: -144 + 144 = 0 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + 168x + -168x + -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 168x + -168x + -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 Combine like terms: 168x + -168x = 0 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = -73x2 + 73x2 + 14x3 + -14x3 + -1x4 + x4 Combine like terms: -73x2 + 73x2 = 0 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + 14x3 + -14x3 + -1x4 + x4 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 14x3 + -14x3 + -1x4 + x4 Combine like terms: 14x3 + -14x3 = 0 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 + -1x4 + x4 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 144 + -81i2 + 54i2x + -9i2x2 + -168x + 73x2 + -14x3 + x4 = 0 The solution to this equation could not be determined.
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