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Simplifying 0 = (t + -3)(t + -2)(t + -3i)(3 + 3i) Reorder the terms: 0 = (-3 + t)(t + -2)(t + -3i)(3 + 3i) Reorder the terms: 0 = (-3 + t)(-2 + t)(t + -3i)(3 + 3i) Reorder the terms: 0 = (-3 + t)(-2 + t)(-3i + t)(3 + 3i) Multiply (-3 + t) * (-2 + t) 0 = (-3(-2 + t) + t(-2 + t))(-3i + t)(3 + 3i) 0 = ((-2 * -3 + t * -3) + t(-2 + t))(-3i + t)(3 + 3i) 0 = ((6 + -3t) + t(-2 + t))(-3i + t)(3 + 3i) 0 = (6 + -3t + (-2 * t + t * t))(-3i + t)(3 + 3i) 0 = (6 + -3t + (-2t + t2))(-3i + t)(3 + 3i) Combine like terms: -3t + -2t = -5t 0 = (6 + -5t + t2)(-3i + t)(3 + 3i) Multiply (6 + -5t + t2) * (-3i + t) 0 = (6(-3i + t) + -5t * (-3i + t) + t2(-3i + t))(3 + 3i) 0 = ((-3i * 6 + t * 6) + -5t * (-3i + t) + t2(-3i + t))(3 + 3i) 0 = ((-18i + 6t) + -5t * (-3i + t) + t2(-3i + t))(3 + 3i) 0 = (-18i + 6t + (-3i * -5t + t * -5t) + t2(-3i + t))(3 + 3i) 0 = (-18i + 6t + (15it + -5t2) + t2(-3i + t))(3 + 3i) 0 = (-18i + 6t + 15it + -5t2 + (-3i * t2 + t * t2))(3 + 3i) 0 = (-18i + 6t + 15it + -5t2 + (-3it2 + t3))(3 + 3i) Reorder the terms: 0 = (-18i + 15it + -3it2 + 6t + -5t2 + t3)(3 + 3i) 0 = (-18i + 15it + -3it2 + 6t + -5t2 + t3)(3 + 3i) Multiply (-18i + 15it + -3it2 + 6t + -5t2 + t3) * (3 + 3i) 0 = (-18i * (3 + 3i) + 15it * (3 + 3i) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = ((3 * -18i + 3i * -18i) + 15it * (3 + 3i) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = ((-54i + -54i2) + 15it * (3 + 3i) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = (-54i + -54i2 + (3 * 15it + 3i * 15it) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = (-54i + -54i2 + (45it + 45i2t) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = (-54i + -54i2 + 45it + 45i2t + (3 * -3it2 + 3i * -3it2) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = (-54i + -54i2 + 45it + 45i2t + (-9it2 + -9i2t2) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + (3 * 6t + 3i * 6t) + -5t2 * (3 + 3i) + t3(3 + 3i)) Reorder the terms: 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + (18it + 18t) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + (18it + 18t) + -5t2 * (3 + 3i) + t3(3 + 3i)) 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + (3 * -5t2 + 3i * -5t2) + t3(3 + 3i)) Reorder the terms: 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + (-15it2 + -15t2) + t3(3 + 3i)) 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + (-15it2 + -15t2) + t3(3 + 3i)) 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + -15it2 + -15t2 + (3 * t3 + 3i * t3)) Reorder the terms: 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + -15it2 + -15t2 + (3it3 + 3t3)) 0 = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + -15it2 + -15t2 + (3it3 + 3t3)) Reorder the terms: 0 = (-54i + 45it + 18it + -9it2 + -15it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3) Combine like terms: 45it + 18it = 63it 0 = (-54i + 63it + -9it2 + -15it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3) Combine like terms: -9it2 + -15it2 = -24it2 0 = (-54i + 63it + -24it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3) Solving 0 = -54i + 63it + -24it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3 Solving for variable 'i'. Remove the zero: 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = -54i + 63it + -24it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3 + 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 Reorder the terms: 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = -54i + 54i + 63it + -63it + -24it2 + 24it2 + 3it3 + -3it3 + -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: -54i + 54i = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + 63it + -63it + -24it2 + 24it2 + 3it3 + -3it3 + -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 63it + -63it + -24it2 + 24it2 + 3it3 + -3it3 + -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: 63it + -63it = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + -24it2 + 24it2 + 3it3 + -3it3 + -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = -24it2 + 24it2 + 3it3 + -3it3 + -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: -24it2 + 24it2 = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + 3it3 + -3it3 + -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 3it3 + -3it3 + -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: 3it3 + -3it3 = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = -54i2 + 54i2 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: -54i2 + 54i2 = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 45i2t + -45i2t + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: 45i2t + -45i2t = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = -9i2t2 + 9i2t2 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: -9i2t2 + 9i2t2 = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 18t + -18t + -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: 18t + -18t = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + -15t2 + 15t2 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = -15t2 + 15t2 + 3t3 + -3t3 Combine like terms: -15t2 + 15t2 = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 + 3t3 + -3t3 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 3t3 + -3t3 Combine like terms: 3t3 + -3t3 = 0 54i + -63it + 24it2 + -3it3 + 54i2 + -45i2t + 9i2t2 + -18t + 15t2 + -3t3 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(18i + -21it + 8it2 + -1it3 + 18i2 + -15i2t + 3i2t2 + -6t + 5t2 + -1t3) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(18i + -21it + 8it2 + -1it3 + 18i2 + -15i2t + 3i2t2 + -6t + 5t2 + -1t3)' equal to zero and attempt to solve: Simplifying 18i + -21it + 8it2 + -1it3 + 18i2 + -15i2t + 3i2t2 + -6t + 5t2 + -1t3 = 0 Solving 18i + -21it + 8it2 + -1it3 + 18i2 + -15i2t + 3i2t2 + -6t + 5t2 + -1t3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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