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Simplifying (x + -3)(x + -3)(x + -4i)(x + 4i) = 0 Reorder the terms: (-3 + x)(x + -3)(x + -4i)(x + 4i) = 0 Reorder the terms: (-3 + x)(-3 + x)(x + -4i)(x + 4i) = 0 Reorder the terms: (-3 + x)(-3 + x)(-4i + x)(x + 4i) = 0 Reorder the terms: (-3 + x)(-3 + x)(-4i + x)(4i + x) = 0 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x))(-4i + x)(4i + x) = 0 ((-3 * -3 + x * -3) + x(-3 + x))(-4i + x)(4i + x) = 0 ((9 + -3x) + x(-3 + x))(-4i + x)(4i + x) = 0 (9 + -3x + (-3 * x + x * x))(-4i + x)(4i + x) = 0 (9 + -3x + (-3x + x2))(-4i + x)(4i + x) = 0 Combine like terms: -3x + -3x = -6x (9 + -6x + x2)(-4i + x)(4i + x) = 0 Multiply (9 + -6x + x2) * (-4i + x) (9(-4i + x) + -6x * (-4i + x) + x2(-4i + x))(4i + x) = 0 ((-4i * 9 + x * 9) + -6x * (-4i + x) + x2(-4i + x))(4i + x) = 0 ((-36i + 9x) + -6x * (-4i + x) + x2(-4i + x))(4i + x) = 0 (-36i + 9x + (-4i * -6x + x * -6x) + x2(-4i + x))(4i + x) = 0 (-36i + 9x + (24ix + -6x2) + x2(-4i + x))(4i + x) = 0 (-36i + 9x + 24ix + -6x2 + (-4i * x2 + x * x2))(4i + x) = 0 (-36i + 9x + 24ix + -6x2 + (-4ix2 + x3))(4i + x) = 0 Reorder the terms: (-36i + 24ix + -4ix2 + 9x + -6x2 + x3)(4i + x) = 0 (-36i + 24ix + -4ix2 + 9x + -6x2 + x3)(4i + x) = 0 Multiply (-36i + 24ix + -4ix2 + 9x + -6x2 + x3) * (4i + x) (-36i * (4i + x) + 24ix * (4i + x) + -4ix2 * (4i + x) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 ((4i * -36i + x * -36i) + 24ix * (4i + x) + -4ix2 * (4i + x) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 Reorder the terms: ((-36ix + -144i2) + 24ix * (4i + x) + -4ix2 * (4i + x) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 ((-36ix + -144i2) + 24ix * (4i + x) + -4ix2 * (4i + x) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 (-36ix + -144i2 + (4i * 24ix + x * 24ix) + -4ix2 * (4i + x) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 Reorder the terms: (-36ix + -144i2 + (24ix2 + 96i2x) + -4ix2 * (4i + x) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 (-36ix + -144i2 + (24ix2 + 96i2x) + -4ix2 * (4i + x) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 (-36ix + -144i2 + 24ix2 + 96i2x + (4i * -4ix2 + x * -4ix2) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 Reorder the terms: (-36ix + -144i2 + 24ix2 + 96i2x + (-4ix3 + -16i2x2) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 (-36ix + -144i2 + 24ix2 + 96i2x + (-4ix3 + -16i2x2) + 9x * (4i + x) + -6x2 * (4i + x) + x3(4i + x)) = 0 (-36ix + -144i2 + 24ix2 + 96i2x + -4ix3 + -16i2x2 + (4i * 9x + x * 9x) + -6x2 * (4i + x) + x3(4i + x)) = 0 (-36ix + -144i2 + 24ix2 + 96i2x + -4ix3 + -16i2x2 + (36ix + 9x2) + -6x2 * (4i + x) + x3(4i + x)) = 0 (-36ix + -144i2 + 24ix2 + 96i2x + -4ix3 + -16i2x2 + 36ix + 9x2 + (4i * -6x2 + x * -6x2) + x3(4i + x)) = 0 (-36ix + -144i2 + 24ix2 + 96i2x + -4ix3 + -16i2x2 + 36ix + 9x2 + (-24ix2 + -6x3) + x3(4i + x)) = 0 (-36ix + -144i2 + 24ix2 + 96i2x + -4ix3 + -16i2x2 + 36ix + 9x2 + -24ix2 + -6x3 + (4i * x3 + x * x3)) = 0 (-36ix + -144i2 + 24ix2 + 96i2x + -4ix3 + -16i2x2 + 36ix + 9x2 + -24ix2 + -6x3 + (4ix3 + x4)) = 0 Reorder the terms: (-36ix + 36ix + 24ix2 + -24ix2 + -4ix3 + 4ix3 + -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4) = 0 Combine like terms: -36ix + 36ix = 0 (0 + 24ix2 + -24ix2 + -4ix3 + 4ix3 + -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4) = 0 (24ix2 + -24ix2 + -4ix3 + 4ix3 + -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4) = 0 Combine like terms: 24ix2 + -24ix2 = 0 (0 + -4ix3 + 4ix3 + -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4) = 0 (-4ix3 + 4ix3 + -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4) = 0 Combine like terms: -4ix3 + 4ix3 = 0 (0 + -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4) = 0 (-144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4) = 0 Solving -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9x2' to each side of the equation. -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + -9x2 + x4 = 0 + -9x2 Reorder the terms: -144i2 + 96i2x + -16i2x2 + 9x2 + -9x2 + -6x3 + x4 = 0 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -144i2 + 96i2x + -16i2x2 + 0 + -6x3 + x4 = 0 + -9x2 -144i2 + 96i2x + -16i2x2 + -6x3 + x4 = 0 + -9x2 Remove the zero: -144i2 + 96i2x + -16i2x2 + -6x3 + x4 = -9x2 Add '6x3' to each side of the equation. -144i2 + 96i2x + -16i2x2 + -6x3 + 6x3 + x4 = -9x2 + 6x3 Combine like terms: -6x3 + 6x3 = 0 -144i2 + 96i2x + -16i2x2 + 0 + x4 = -9x2 + 6x3 -144i2 + 96i2x + -16i2x2 + x4 = -9x2 + 6x3 Add '-1x4' to each side of the equation. -144i2 + 96i2x + -16i2x2 + x4 + -1x4 = -9x2 + 6x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -144i2 + 96i2x + -16i2x2 + 0 = -9x2 + 6x3 + -1x4 -144i2 + 96i2x + -16i2x2 = -9x2 + 6x3 + -1x4 Reorder the terms: -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4 = -9x2 + 9x2 + 6x3 + -6x3 + -1x4 + x4 Combine like terms: -9x2 + 9x2 = 0 -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4 = 0 + 6x3 + -6x3 + -1x4 + x4 -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4 = 6x3 + -6x3 + -1x4 + x4 Combine like terms: 6x3 + -6x3 = 0 -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4 = 0 + -1x4 + x4 -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -144i2 + 96i2x + -16i2x2 + 9x2 + -6x3 + x4 = 0 The solution to this equation could not be determined.
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