H(t)=32.83t-4.9t^2

Solution for H(t)=32.83t-4.9t^2 equation:

Simplifying
H(t) = 32.83t + -4.9t2

Multiply H * t
tH = 32.83t + -4.9t2

Solving
tH = 32.83t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-32.83t + tH + 4.9t2 = 32.83t + -4.9t2 + -32.83t + 4.9t2

Reorder the terms:
-32.83t + tH + 4.9t2 = 32.83t + -32.83t + -4.9t2 + 4.9t2

Combine like terms: 32.83t + -32.83t = 0.00
-32.83t + tH + 4.9t2 = 0.00 + -4.9t2 + 4.9t2
-32.83t + tH + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-32.83t + tH + 4.9t2 = 0.0

Factor out the Greatest Common Factor (GCF), 't'.
t(-32.83 + H + 4.9t) = 0.0

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 '(-32.83 + H + 4.9t)' equal to zero and attempt to solve:

Simplifying
-32.83 + H + 4.9t = 0

Solving
-32.83 + H + 4.9t = 0

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

Add '32.83' to each side of the equation.
-32.83 + H + 32.83 + 4.9t = 0 + 32.83

Reorder the terms:
-32.83 + 32.83 + H + 4.9t = 0 + 32.83

Combine like terms: -32.83 + 32.83 = 0.00
0.00 + H + 4.9t = 0 + 32.83
H + 4.9t = 0 + 32.83

Combine like terms: 0 + 32.83 = 32.83
H + 4.9t = 32.83

Add '-1H' to each side of the equation.
H + -1H + 4.9t = 32.83 + -1H

Combine like terms: H + -1H = 0
0 + 4.9t = 32.83 + -1H
4.9t = 32.83 + -1H

Divide each side by '4.9'.
t = 6.7 + -0.2040816327H

Simplifying
t = 6.7 + -0.2040816327H
Solution
t = {0, 6.7 + -0.2040816327H}