H(t)=12t-3t^2

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Solution for H(t)=12t-3t^2 equation:


Simplifying
H(t) = 12t + -3t2

Multiply H * t
tH = 12t + -3t2

Solving
tH = 12t + -3t2

Solving for variable 't'.

Reorder the terms:
-12t + tH + 3t2 = 12t + -3t2 + -12t + 3t2

Reorder the terms:
-12t + tH + 3t2 = 12t + -12t + -3t2 + 3t2

Combine like terms: 12t + -12t = 0
-12t + tH + 3t2 = 0 + -3t2 + 3t2
-12t + tH + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
-12t + tH + 3t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-12 + H + 3t) = 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 '(-12 + H + 3t)' equal to zero and attempt to solve: Simplifying -12 + H + 3t = 0 Solving -12 + H + 3t = 0 Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + H + 12 + 3t = 0 + 12 Reorder the terms: -12 + 12 + H + 3t = 0 + 12 Combine like terms: -12 + 12 = 0 0 + H + 3t = 0 + 12 H + 3t = 0 + 12 Combine like terms: 0 + 12 = 12 H + 3t = 12 Add '-1H' to each side of the equation. H + -1H + 3t = 12 + -1H Combine like terms: H + -1H = 0 0 + 3t = 12 + -1H 3t = 12 + -1H Divide each side by '3'. t = 4 + -0.3333333333H Simplifying t = 4 + -0.3333333333H

Solution

t = {0, 4 + -0.3333333333H}

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