h(t)=(t-3)(t-2)(t-3i)(3+3i)

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Solution for h(t)=(t-3)(t-2)(t-3i)(3+3i) equation: 


Simplifying
h(t) = (t + -3)(t + -2)(t + -3i)(3 + 3i)

Multiply h * t
ht = (t + -3)(t + -2)(t + -3i)(3 + 3i)

Reorder the terms:
ht = (-3 + t)(t + -2)(t + -3i)(3 + 3i)

Reorder the terms:
ht = (-3 + t)(-2 + t)(t + -3i)(3 + 3i)

Reorder the terms:
ht = (-3 + t)(-2 + t)(-3i + t)(3 + 3i)

Multiply (-3 + t) * (-2 + t)
ht = (-3(-2 + t) + t(-2 + t))(-3i + t)(3 + 3i)
ht = ((-2 * -3 + t * -3) + t(-2 + t))(-3i + t)(3 + 3i)
ht = ((6 + -3t) + t(-2 + t))(-3i + t)(3 + 3i)
ht = (6 + -3t + (-2 * t + t * t))(-3i + t)(3 + 3i)
ht = (6 + -3t + (-2t + t2))(-3i + t)(3 + 3i)

Combine like terms: -3t + -2t = -5t
ht = (6 + -5t + t2)(-3i + t)(3 + 3i)

Multiply (6 + -5t + t2) * (-3i + t)
ht = (6(-3i + t) + -5t * (-3i + t) + t2(-3i + t))(3 + 3i)
ht = ((-3i * 6 + t * 6) + -5t * (-3i + t) + t2(-3i + t))(3 + 3i)
ht = ((-18i + 6t) + -5t * (-3i + t) + t2(-3i + t))(3 + 3i)
ht = (-18i + 6t + (-3i * -5t + t * -5t) + t2(-3i + t))(3 + 3i)
ht = (-18i + 6t + (15it + -5t2) + t2(-3i + t))(3 + 3i)
ht = (-18i + 6t + 15it + -5t2 + (-3i * t2 + t * t2))(3 + 3i)
ht = (-18i + 6t + 15it + -5t2 + (-3it2 + t3))(3 + 3i)

Reorder the terms:
ht = (-18i + 15it + -3it2 + 6t + -5t2 + t3)(3 + 3i)
ht = (-18i + 15it + -3it2 + 6t + -5t2 + t3)(3 + 3i)

Multiply (-18i + 15it + -3it2 + 6t + -5t2 + t3) * (3 + 3i)
ht = (-18i * (3 + 3i) + 15it * (3 + 3i) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = ((3 * -18i + 3i * -18i) + 15it * (3 + 3i) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = ((-54i + -54i2) + 15it * (3 + 3i) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = (-54i + -54i2 + (3 * 15it + 3i * 15it) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = (-54i + -54i2 + (45it + 45i2t) + -3it2 * (3 + 3i) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = (-54i + -54i2 + 45it + 45i2t + (3 * -3it2 + 3i * -3it2) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = (-54i + -54i2 + 45it + 45i2t + (-9it2 + -9i2t2) + 6t * (3 + 3i) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + (3 * 6t + 3i * 6t) + -5t2 * (3 + 3i) + t3(3 + 3i))

Reorder the terms:
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + (18it + 18t) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + (18it + 18t) + -5t2 * (3 + 3i) + t3(3 + 3i))
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + (3 * -5t2 + 3i * -5t2) + t3(3 + 3i))

Reorder the terms:
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + (-15it2 + -15t2) + t3(3 + 3i))
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + (-15it2 + -15t2) + t3(3 + 3i))
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + -15it2 + -15t2 + (3 * t3 + 3i * t3))

Reorder the terms:
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + -15it2 + -15t2 + (3it3 + 3t3))
ht = (-54i + -54i2 + 45it + 45i2t + -9it2 + -9i2t2 + 18it + 18t + -15it2 + -15t2 + (3it3 + 3t3))

Reorder the terms:
ht = (-54i + 45it + 18it + -9it2 + -15it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3)

Combine like terms: 45it + 18it = 63it
ht = (-54i + 63it + -9it2 + -15it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3)

Combine like terms: -9it2 + -15it2 = -24it2
ht = (-54i + 63it + -24it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3)

Solving
ht = -54i + 63it + -24it2 + 3it3 + -54i2 + 45i2t + -9i2t2 + 18t + -15t2 + 3t3

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Divide each side by 't'.
h = -54it-1 + 63i + -24it + 3it2 + -54i2t-1 + 45i2 + -9i2t + 18 + -15t + 3t2

Simplifying
h = -54it-1 + 63i + -24it + 3it2 + -54i2t-1 + 45i2 + -9i2t + 18 + -15t + 3t2

Reorder the terms:
h = 18 + 63i + -54it-1 + -24it + 3it2 + 45i2 + -54i2t-1 + -9i2t + -15t + 3t2

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