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Simplifying H(t) = -8t2 + 12t Multiply H * t tH = -8t2 + 12t Reorder the terms: tH = 12t + -8t2 Solving tH = 12t + -8t2 Solving for variable 't'. Reorder the terms: -12t + tH + 8t2 = 12t + -8t2 + -12t + 8t2 Reorder the terms: -12t + tH + 8t2 = 12t + -12t + -8t2 + 8t2 Combine like terms: 12t + -12t = 0 -12t + tH + 8t2 = 0 + -8t2 + 8t2 -12t + tH + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 -12t + tH + 8t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-12 + H + 8t) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(-12 + H + 8t)' equal to zero and attempt to solve: Simplifying -12 + H + 8t = 0 Solving -12 + H + 8t = 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 + 8t = 0 + 12 Reorder the terms: -12 + 12 + H + 8t = 0 + 12 Combine like terms: -12 + 12 = 0 0 + H + 8t = 0 + 12 H + 8t = 0 + 12 Combine like terms: 0 + 12 = 12 H + 8t = 12 Add '-1H' to each side of the equation. H + -1H + 8t = 12 + -1H Combine like terms: H + -1H = 0 0 + 8t = 12 + -1H 8t = 12 + -1H Divide each side by '8'. t = 1.5 + -0.125H Simplifying t = 1.5 + -0.125HSolution
t = {0, 1.5 + -0.125H}
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