H(t)=100t-2t^2

Solution for H(t)=100t-2t^2 equation:

Simplifying
H(t) = 100t + -2t2

Multiply H * t
tH = 100t + -2t2

Solving
tH = 100t + -2t2

Solving for variable 't'.

Reorder the terms:
-100t + tH + 2t2 = 100t + -2t2 + -100t + 2t2

Reorder the terms:
-100t + tH + 2t2 = 100t + -100t + -2t2 + 2t2

Combine like terms: 100t + -100t = 0
-100t + tH + 2t2 = 0 + -2t2 + 2t2
-100t + tH + 2t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
-100t + tH + 2t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-100 + H + 2t) = 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 '(-100 + H + 2t)' equal to zero and attempt to solve:

Simplifying
-100 + H + 2t = 0

Solving
-100 + H + 2t = 0

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

Add '100' to each side of the equation.
-100 + H + 100 + 2t = 0 + 100

Reorder the terms:
-100 + 100 + H + 2t = 0 + 100

Combine like terms: -100 + 100 = 0
0 + H + 2t = 0 + 100
H + 2t = 0 + 100

Combine like terms: 0 + 100 = 100
H + 2t = 100

Add '-1H' to each side of the equation.
H + -1H + 2t = 100 + -1H

Combine like terms: H + -1H = 0
0 + 2t = 100 + -1H
2t = 100 + -1H

Divide each side by '2'.
t = 50 + -0.5H

Simplifying
t = 50 + -0.5H
Solution
t = {0, 50 + -0.5H}