H(t)=-16t(t-8)

Solution for H(t)=-16t(t-8) equation:

Simplifying
H(t) = -16t(t + -8)

Multiply H * t
tH = -16t(t + -8)

Reorder the terms:
tH = -16t(-8 + t)
tH = (-8 * -16t + t * -16t)
tH = (128t + -16t2)

Solving
tH = 128t + -16t2

Solving for variable 't'.

Reorder the terms:
-128t + tH + 16t2 = 128t + -16t2 + -128t + 16t2

Reorder the terms:
-128t + tH + 16t2 = 128t + -128t + -16t2 + 16t2

Combine like terms: 128t + -128t = 0
-128t + tH + 16t2 = 0 + -16t2 + 16t2
-128t + tH + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-128t + tH + 16t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-128 + H + 16t) = 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 '(-128 + H + 16t)' equal to zero and attempt to solve:

Simplifying
-128 + H + 16t = 0

Solving
-128 + H + 16t = 0

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

Add '128' to each side of the equation.
-128 + H + 128 + 16t = 0 + 128

Reorder the terms:
-128 + 128 + H + 16t = 0 + 128

Combine like terms: -128 + 128 = 0
0 + H + 16t = 0 + 128
H + 16t = 0 + 128

Combine like terms: 0 + 128 = 128
H + 16t = 128

Add '-1H' to each side of the equation.
H + -1H + 16t = 128 + -1H

Combine like terms: H + -1H = 0
0 + 16t = 128 + -1H
16t = 128 + -1H

Divide each side by '16'.
t = 8 + -0.0625H

Simplifying
t = 8 + -0.0625H
Solution
t = {0, 8 + -0.0625H}