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Simplifying (x + -3)(x + -3)(x + -1 + -1i) = 0 Reorder the terms: (-3 + x)(x + -3)(x + -1 + -1i) = 0 Reorder the terms: (-3 + x)(-3 + x)(x + -1 + -1i) = 0 Reorder the terms: (-3 + x)(-3 + x)(-1 + -1i + x) = 0 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x))(-1 + -1i + x) = 0 ((-3 * -3 + x * -3) + x(-3 + x))(-1 + -1i + x) = 0 ((9 + -3x) + x(-3 + x))(-1 + -1i + x) = 0 (9 + -3x + (-3 * x + x * x))(-1 + -1i + x) = 0 (9 + -3x + (-3x + x2))(-1 + -1i + x) = 0 Combine like terms: -3x + -3x = -6x (9 + -6x + x2)(-1 + -1i + x) = 0 Multiply (9 + -6x + x2) * (-1 + -1i + x) (9(-1 + -1i + x) + -6x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 ((-1 * 9 + -1i * 9 + x * 9) + -6x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 ((-9 + -9i + 9x) + -6x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0 (-9 + -9i + 9x + (-1 * -6x + -1i * -6x + x * -6x) + x2(-1 + -1i + x)) = 0 Reorder the terms: (-9 + -9i + 9x + (6ix + 6x + -6x2) + x2(-1 + -1i + x)) = 0 (-9 + -9i + 9x + (6ix + 6x + -6x2) + x2(-1 + -1i + x)) = 0 (-9 + -9i + 9x + 6ix + 6x + -6x2 + (-1 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-9 + -9i + 9x + 6ix + 6x + -6x2 + (-1ix2 + -1x2 + x3)) = 0 (-9 + -9i + 9x + 6ix + 6x + -6x2 + (-1ix2 + -1x2 + x3)) = 0 Reorder the terms: (-9 + -9i + 6ix + -1ix2 + 9x + 6x + -6x2 + -1x2 + x3) = 0 Combine like terms: 9x + 6x = 15x (-9 + -9i + 6ix + -1ix2 + 15x + -6x2 + -1x2 + x3) = 0 Combine like terms: -6x2 + -1x2 = -7x2 (-9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3) = 0 Solving -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '9' to each side of the equation. -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + 9 + x3 = 0 + 9 Reorder the terms: -9 + 9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 0 + 9 -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 0 + 9 Combine like terms: 0 + 9 = 9 -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 9 Add '-15x' to each side of the equation. -9i + 6ix + -1ix2 + 15x + -7x2 + -15x + x3 = 9 + -15x Reorder the terms: -9i + 6ix + -1ix2 + 15x + -15x + -7x2 + x3 = 9 + -15x Combine like terms: 15x + -15x = 0 -9i + 6ix + -1ix2 + 0 + -7x2 + x3 = 9 + -15x -9i + 6ix + -1ix2 + -7x2 + x3 = 9 + -15x Add '7x2' to each side of the equation. -9i + 6ix + -1ix2 + -7x2 + 7x2 + x3 = 9 + -15x + 7x2 Combine like terms: -7x2 + 7x2 = 0 -9i + 6ix + -1ix2 + 0 + x3 = 9 + -15x + 7x2 -9i + 6ix + -1ix2 + x3 = 9 + -15x + 7x2 Add '-1x3' to each side of the equation. -9i + 6ix + -1ix2 + x3 + -1x3 = 9 + -15x + 7x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -9i + 6ix + -1ix2 + 0 = 9 + -15x + 7x2 + -1x3 -9i + 6ix + -1ix2 = 9 + -15x + 7x2 + -1x3 Reorder the terms: -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 9 + -15x + 7x2 + -1x3 + -9 + 15x + -7x2 + x3 Reorder the terms: -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 9 + -9 + -15x + 15x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: 9 + -9 = 0 -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 0 + -15x + 15x + 7x2 + -7x2 + -1x3 + x3 -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = -15x + 15x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: -15x + 15x = 0 -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 0 + 7x2 + -7x2 + -1x3 + x3 -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 7x2 + -7x2 + -1x3 + x3 Combine like terms: 7x2 + -7x2 = 0 -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 0 + -1x3 + x3 -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -9 + -9i + 6ix + -1ix2 + 15x + -7x2 + x3 = 0 The solution to this equation could not be determined.
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