H(t)=18t-6t^2

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Solution for H(t)=18t-6t^2 equation: 


Simplifying
H(t) = 18t + -6t2

Multiply H * t
tH = 18t + -6t2

Solving
tH = 18t + -6t2

Solving for variable 't'.

Reorder the terms:
-18t + tH + 6t2 = 18t + -6t2 + -18t + 6t2

Reorder the terms:
-18t + tH + 6t2 = 18t + -18t + -6t2 + 6t2

Combine like terms: 18t + -18t = 0
-18t + tH + 6t2 = 0 + -6t2 + 6t2
-18t + tH + 6t2 = -6t2 + 6t2

Combine like terms: -6t2 + 6t2 = 0
-18t + tH + 6t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-18 + H + 6t) = 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 '(-18 + H + 6t)' equal to zero and attempt to solve:

Simplifying
-18 + H + 6t = 0

Solving
-18 + H + 6t = 0

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

Add '18' to each side of the equation.
-18 + H + 18 + 6t = 0 + 18

Reorder the terms:
-18 + 18 + H + 6t = 0 + 18

Combine like terms: -18 + 18 = 0
0 + H + 6t = 0 + 18
H + 6t = 0 + 18

Combine like terms: 0 + 18 = 18
H + 6t = 18

Add '-1H' to each side of the equation.
H + -1H + 6t = 18 + -1H

Combine like terms: H + -1H = 0
0 + 6t = 18 + -1H
6t = 18 + -1H

Divide each side by '6'.
t = 3 + -0.1666666667H

Simplifying
t = 3 + -0.1666666667H
Solution
t = {0, 3 + -0.1666666667H}

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