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Simplifying F(t) = 5t + 3e2t Multiply F * t tF = 5t + 3e2t Reorder the terms: tF = 3e2t + 5t Solving tF = 3e2t + 5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3e2t' to each side of the equation. -3e2t + tF = 3e2t + -3e2t + 5t Combine like terms: 3e2t + -3e2t = 0 -3e2t + tF = 0 + 5t -3e2t + tF = 5t Add '-5t' to each side of the equation. -3e2t + -5t + tF = 5t + -5t Combine like terms: 5t + -5t = 0 -3e2t + -5t + tF = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-3e2 + -5 + F) = 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 '(-3e2 + -5 + F)' equal to zero and attempt to solve: Simplifying -3e2 + -5 + F = 0 Reorder the terms: -5 + F + -3e2 = 0 Solving -5 + F + -3e2 = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + F + 5 + -3e2 = 0 + 5 Reorder the terms: -5 + 5 + F + -3e2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + F + -3e2 = 0 + 5 F + -3e2 = 0 + 5 Combine like terms: 0 + 5 = 5 F + -3e2 = 5 Add '-1F' to each side of the equation. F + -1F + -3e2 = 5 + -1F Combine like terms: F + -1F = 0 0 + -3e2 = 5 + -1F -3e2 = 5 + -1F Add '3e2' to each side of the equation. -3e2 + 3e2 = 5 + -1F + 3e2 Combine like terms: -3e2 + 3e2 = 0 0 = 5 + -1F + 3e2 Simplifying 0 = 5 + -1F + 3e2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
t = {0}
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