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Simplifying H(t) = -3t2 + 4t Multiply H * t tH = -3t2 + 4t Reorder the terms: tH = 4t + -3t2 Solving tH = 4t + -3t2 Solving for variable 't'. Reorder the terms: -4t + tH + 3t2 = 4t + -3t2 + -4t + 3t2 Reorder the terms: -4t + tH + 3t2 = 4t + -4t + -3t2 + 3t2 Combine like terms: 4t + -4t = 0 -4t + tH + 3t2 = 0 + -3t2 + 3t2 -4t + tH + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 -4t + tH + 3t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-4 + H + 3t) = 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 '(-4 + H + 3t)' equal to zero and attempt to solve: Simplifying -4 + H + 3t = 0 Solving -4 + H + 3t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + H + 4 + 3t = 0 + 4 Reorder the terms: -4 + 4 + H + 3t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + H + 3t = 0 + 4 H + 3t = 0 + 4 Combine like terms: 0 + 4 = 4 H + 3t = 4 Add '-1H' to each side of the equation. H + -1H + 3t = 4 + -1H Combine like terms: H + -1H = 0 0 + 3t = 4 + -1H 3t = 4 + -1H Divide each side by '3'. t = 1.333333333 + -0.3333333333H Simplifying t = 1.333333333 + -0.3333333333HSolution
t = {0, 1.333333333 + -0.3333333333H}
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