H(t)=-5t^2+120t

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Solution for H(t)=-5t^2+120t equation: 


Simplifying
H(t) = -5t2 + 120t

Multiply H * t
tH = -5t2 + 120t

Reorder the terms:
tH = 120t + -5t2

Solving
tH = 120t + -5t2

Solving for variable 't'.

Reorder the terms:
-120t + tH + 5t2 = 120t + -5t2 + -120t + 5t2

Reorder the terms:
-120t + tH + 5t2 = 120t + -120t + -5t2 + 5t2

Combine like terms: 120t + -120t = 0
-120t + tH + 5t2 = 0 + -5t2 + 5t2
-120t + tH + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-120t + tH + 5t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-120 + H + 5t) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

Subproblem 2
Set the factor '(-120 + H + 5t)' equal to zero and attempt to solve:

Simplifying
-120 + H + 5t = 0

Solving
-120 + H + 5t = 0

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

Add '120' to each side of the equation.
-120 + H + 120 + 5t = 0 + 120

Reorder the terms:
-120 + 120 + H + 5t = 0 + 120

Combine like terms: -120 + 120 = 0
0 + H + 5t = 0 + 120
H + 5t = 0 + 120

Combine like terms: 0 + 120 = 120
H + 5t = 120

Add '-1H' to each side of the equation.
H + -1H + 5t = 120 + -1H

Combine like terms: H + -1H = 0
0 + 5t = 120 + -1H
5t = 120 + -1H

Divide each side by '5'.
t = 24 + -0.2H

Simplifying
t = 24 + -0.2H
Solution
t = {0, 24 + -0.2H}

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