f(t)=(5t^3+t^2)(2t-4)

Solution for f(t)=(5t^3+t^2)(2t-4) equation:

Simplifying
f(t) = (5t3 + t2)(2t + -4)

Multiply f * t
ft = (5t3 + t2)(2t + -4)

Reorder the terms:
ft = (t2 + 5t3)(2t + -4)

Reorder the terms:
ft = (t2 + 5t3)(-4 + 2t)

Multiply (t2 + 5t3) * (-4 + 2t)
ft = (t2(-4 + 2t) + 5t3 * (-4 + 2t))
ft = ((-4 * t2 + 2t * t2) + 5t3 * (-4 + 2t))
ft = ((-4t2 + 2t3) + 5t3 * (-4 + 2t))
ft = (-4t2 + 2t3 + (-4 * 5t3 + 2t * 5t3))
ft = (-4t2 + 2t3 + (-20t3 + 10t4))

Combine like terms: 2t3 + -20t3 = -18t3
ft = (-4t2 + -18t3 + 10t4)

Solving
ft = -4t2 + -18t3 + 10t4

Solving for variable 'f'.

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

Divide each side by 't'.
f = -4t + -18t2 + 10t3

Simplifying
f = -4t + -18t2 + 10t3