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Simplifying H(t) = -6t2 + 40t Multiply H * t tH = -6t2 + 40t Reorder the terms: tH = 40t + -6t2 Solving tH = 40t + -6t2 Solving for variable 't'. Reorder the terms: -40t + tH + 6t2 = 40t + -6t2 + -40t + 6t2 Reorder the terms: -40t + tH + 6t2 = 40t + -40t + -6t2 + 6t2 Combine like terms: 40t + -40t = 0 -40t + tH + 6t2 = 0 + -6t2 + 6t2 -40t + tH + 6t2 = -6t2 + 6t2 Combine like terms: -6t2 + 6t2 = 0 -40t + tH + 6t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-40 + H + 6t) = 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 '(-40 + H + 6t)' equal to zero and attempt to solve: Simplifying -40 + H + 6t = 0 Solving -40 + H + 6t = 0 Move all terms containing t to the left, all other terms to the right. Add '40' to each side of the equation. -40 + H + 40 + 6t = 0 + 40 Reorder the terms: -40 + 40 + H + 6t = 0 + 40 Combine like terms: -40 + 40 = 0 0 + H + 6t = 0 + 40 H + 6t = 0 + 40 Combine like terms: 0 + 40 = 40 H + 6t = 40 Add '-1H' to each side of the equation. H + -1H + 6t = 40 + -1H Combine like terms: H + -1H = 0 0 + 6t = 40 + -1H 6t = 40 + -1H Divide each side by '6'. t = 6.666666667 + -0.1666666667H Simplifying t = 6.666666667 + -0.1666666667HSolution
t = {0, 6.666666667 + -0.1666666667H}
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