f(t)=(t-2)(t-2)(t-2)-(t-2)

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Solution for f(t)=(t-2)(t-2)(t-2)-(t-2) equation: 


Simplifying
f(t) = (t + -2)(t + -2)(t + -2) + -1(t + -2)

Multiply f * t
ft = (t + -2)(t + -2)(t + -2) + -1(t + -2)

Reorder the terms:
ft = (-2 + t)(t + -2)(t + -2) + -1(t + -2)

Reorder the terms:
ft = (-2 + t)(-2 + t)(t + -2) + -1(t + -2)

Reorder the terms:
ft = (-2 + t)(-2 + t)(-2 + t) + -1(t + -2)

Multiply (-2 + t) * (-2 + t)
ft = (-2(-2 + t) + t(-2 + t))(-2 + t) + -1(t + -2)
ft = ((-2 * -2 + t * -2) + t(-2 + t))(-2 + t) + -1(t + -2)
ft = ((4 + -2t) + t(-2 + t))(-2 + t) + -1(t + -2)
ft = (4 + -2t + (-2 * t + t * t))(-2 + t) + -1(t + -2)
ft = (4 + -2t + (-2t + t2))(-2 + t) + -1(t + -2)

Combine like terms: -2t + -2t = -4t
ft = (4 + -4t + t2)(-2 + t) + -1(t + -2)

Multiply (4 + -4t + t2) * (-2 + t)
ft = (4(-2 + t) + -4t * (-2 + t) + t2(-2 + t)) + -1(t + -2)
ft = ((-2 * 4 + t * 4) + -4t * (-2 + t) + t2(-2 + t)) + -1(t + -2)
ft = ((-8 + 4t) + -4t * (-2 + t) + t2(-2 + t)) + -1(t + -2)
ft = (-8 + 4t + (-2 * -4t + t * -4t) + t2(-2 + t)) + -1(t + -2)
ft = (-8 + 4t + (8t + -4t2) + t2(-2 + t)) + -1(t + -2)
ft = (-8 + 4t + 8t + -4t2 + (-2 * t2 + t * t2)) + -1(t + -2)
ft = (-8 + 4t + 8t + -4t2 + (-2t2 + t3)) + -1(t + -2)

Combine like terms: 4t + 8t = 12t
ft = (-8 + 12t + -4t2 + -2t2 + t3) + -1(t + -2)

Combine like terms: -4t2 + -2t2 = -6t2
ft = (-8 + 12t + -6t2 + t3) + -1(t + -2)

Reorder the terms:
ft = -8 + 12t + -6t2 + t3 + -1(-2 + t)
ft = -8 + 12t + -6t2 + t3 + (-2 * -1 + t * -1)
ft = -8 + 12t + -6t2 + t3 + (2 + -1t)

Reorder the terms:
ft = -8 + 2 + 12t + -1t + -6t2 + t3

Combine like terms: -8 + 2 = -6
ft = -6 + 12t + -1t + -6t2 + t3

Combine like terms: 12t + -1t = 11t
ft = -6 + 11t + -6t2 + t3

Solving
ft = -6 + 11t + -6t2 + t3

Solving for variable 'f'.

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

Divide each side by 't'.
f = -6t-1 + 11 + -6t + t2

Simplifying
f = -6t-1 + 11 + -6t + t2

Reorder the terms:
f = 11 + -6t-1 + -6t + t2

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