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Simplifying Tn = n(5n + 4) Reorder the terms: nT = n(4 + 5n) nT = (4 * n + 5n * n) nT = (4n + 5n2) Solving nT = 4n + 5n2 Solving for variable 'n'. Reorder the terms: -4n + nT + -5n2 = 4n + 5n2 + -4n + -5n2 Reorder the terms: -4n + nT + -5n2 = 4n + -4n + 5n2 + -5n2 Combine like terms: 4n + -4n = 0 -4n + nT + -5n2 = 0 + 5n2 + -5n2 -4n + nT + -5n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 -4n + nT + -5n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-4 + 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 '(-4 + T + -5n)' equal to zero and attempt to solve: Simplifying -4 + T + -5n = 0 Solving -4 + T + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + T + 4 + -5n = 0 + 4 Reorder the terms: -4 + 4 + T + -5n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + T + -5n = 0 + 4 T + -5n = 0 + 4 Combine like terms: 0 + 4 = 4 T + -5n = 4 Add '-1T' to each side of the equation. T + -1T + -5n = 4 + -1T Combine like terms: T + -1T = 0 0 + -5n = 4 + -1T -5n = 4 + -1T Divide each side by '-5'. n = -0.8 + 0.2T Simplifying n = -0.8 + 0.2TSolution
n = {0, -0.8 + 0.2T}
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