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Simplifying tn = n(5n + -9) Reorder the terms: nt = n(-9 + 5n) nt = (-9 * n + 5n * n) nt = (-9n + 5n2) Solving nt = -9n + 5n2 Solving for variable 'n'. Reorder the terms: 9n + nt + -5n2 = -9n + 5n2 + 9n + -5n2 Reorder the terms: 9n + nt + -5n2 = -9n + 9n + 5n2 + -5n2 Combine like terms: -9n + 9n = 0 9n + nt + -5n2 = 0 + 5n2 + -5n2 9n + nt + -5n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 9n + nt + -5n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(9 + t + -5n) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(9 + t + -5n)' equal to zero and attempt to solve: Simplifying 9 + t + -5n = 0 Reorder the terms: 9 + -5n + t = 0 Solving 9 + -5n + t = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -5n + -9 + t = 0 + -9 Reorder the terms: 9 + -9 + -5n + t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5n + t = 0 + -9 -5n + t = 0 + -9 Combine like terms: 0 + -9 = -9 -5n + t = -9 Add '-1t' to each side of the equation. -5n + t + -1t = -9 + -1t Combine like terms: t + -1t = 0 -5n + 0 = -9 + -1t -5n = -9 + -1t Divide each side by '-5'. n = 1.8 + 0.2t Simplifying n = 1.8 + 0.2tSolution
n = {0, 1.8 + 0.2t}
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