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Simplifying (x2 + 5x + 6)(x2 + -4x + 3xi + -12i) = 0 Reorder the terms: (6 + 5x + x2)(x2 + -4x + 3xi + -12i) = 0 Reorder the terms: (6 + 5x + x2)(-12i + 3ix + -4x + x2) = 0 Multiply (6 + 5x + x2) * (-12i + 3ix + -4x + x2) (6(-12i + 3ix + -4x + x2) + 5x * (-12i + 3ix + -4x + x2) + x2(-12i + 3ix + -4x + x2)) = 0 ((-12i * 6 + 3ix * 6 + -4x * 6 + x2 * 6) + 5x * (-12i + 3ix + -4x + x2) + x2(-12i + 3ix + -4x + x2)) = 0 ((-72i + 18ix + -24x + 6x2) + 5x * (-12i + 3ix + -4x + x2) + x2(-12i + 3ix + -4x + x2)) = 0 (-72i + 18ix + -24x + 6x2 + (-12i * 5x + 3ix * 5x + -4x * 5x + x2 * 5x) + x2(-12i + 3ix + -4x + x2)) = 0 (-72i + 18ix + -24x + 6x2 + (-60ix + 15ix2 + -20x2 + 5x3) + x2(-12i + 3ix + -4x + x2)) = 0 (-72i + 18ix + -24x + 6x2 + -60ix + 15ix2 + -20x2 + 5x3 + (-12i * x2 + 3ix * x2 + -4x * x2 + x2 * x2)) = 0 (-72i + 18ix + -24x + 6x2 + -60ix + 15ix2 + -20x2 + 5x3 + (-12ix2 + 3ix3 + -4x3 + x4)) = 0 Reorder the terms: (-72i + 18ix + -60ix + 15ix2 + -12ix2 + 3ix3 + -24x + 6x2 + -20x2 + 5x3 + -4x3 + x4) = 0 Combine like terms: 18ix + -60ix = -42ix (-72i + -42ix + 15ix2 + -12ix2 + 3ix3 + -24x + 6x2 + -20x2 + 5x3 + -4x3 + x4) = 0 Combine like terms: 15ix2 + -12ix2 = 3ix2 (-72i + -42ix + 3ix2 + 3ix3 + -24x + 6x2 + -20x2 + 5x3 + -4x3 + x4) = 0 Combine like terms: 6x2 + -20x2 = -14x2 (-72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + 5x3 + -4x3 + x4) = 0 Combine like terms: 5x3 + -4x3 = 1x3 (-72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + 1x3 + x4) = 0 Solving -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + 1x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '24x' to each side of the equation. -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + 1x3 + 24x + x4 = 0 + 24x Reorder the terms: -72i + -42ix + 3ix2 + 3ix3 + -24x + 24x + -14x2 + 1x3 + x4 = 0 + 24x Combine like terms: -24x + 24x = 0 -72i + -42ix + 3ix2 + 3ix3 + 0 + -14x2 + 1x3 + x4 = 0 + 24x -72i + -42ix + 3ix2 + 3ix3 + -14x2 + 1x3 + x4 = 0 + 24x Remove the zero: -72i + -42ix + 3ix2 + 3ix3 + -14x2 + 1x3 + x4 = 24x Add '14x2' to each side of the equation. -72i + -42ix + 3ix2 + 3ix3 + -14x2 + 1x3 + 14x2 + x4 = 24x + 14x2 Reorder the terms: -72i + -42ix + 3ix2 + 3ix3 + -14x2 + 14x2 + 1x3 + x4 = 24x + 14x2 Combine like terms: -14x2 + 14x2 = 0 -72i + -42ix + 3ix2 + 3ix3 + 0 + 1x3 + x4 = 24x + 14x2 -72i + -42ix + 3ix2 + 3ix3 + 1x3 + x4 = 24x + 14x2 Add '-1x3' to each side of the equation. -72i + -42ix + 3ix2 + 3ix3 + 1x3 + -1x3 + x4 = 24x + 14x2 + -1x3 Combine like terms: 1x3 + -1x3 = 0 -72i + -42ix + 3ix2 + 3ix3 + 0 + x4 = 24x + 14x2 + -1x3 -72i + -42ix + 3ix2 + 3ix3 + x4 = 24x + 14x2 + -1x3 Add '-1x4' to each side of the equation. -72i + -42ix + 3ix2 + 3ix3 + x4 + -1x4 = 24x + 14x2 + -1x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -72i + -42ix + 3ix2 + 3ix3 + 0 = 24x + 14x2 + -1x3 + -1x4 -72i + -42ix + 3ix2 + 3ix3 = 24x + 14x2 + -1x3 + -1x4 Reorder the terms: -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + x3 + x4 = 24x + -24x + 14x2 + -14x2 + -1x3 + x3 + -1x4 + x4 Combine like terms: 24x + -24x = 0 -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + x3 + x4 = 0 + 14x2 + -14x2 + -1x3 + x3 + -1x4 + x4 -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + x3 + x4 = 14x2 + -14x2 + -1x3 + x3 + -1x4 + x4 Combine like terms: 14x2 + -14x2 = 0 -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + x3 + x4 = 0 + -1x3 + x3 + -1x4 + x4 -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + x3 + x4 = -1x3 + x3 + -1x4 + x4 Combine like terms: -1x3 + x3 = 0 -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + x3 + x4 = 0 + -1x4 + x4 -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -72i + -42ix + 3ix2 + 3ix3 + -24x + -14x2 + x3 + x4 = 0 The solution to this equation could not be determined.
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