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Simplifying Tn = 2n2 + -4n Reorder the terms: nT = -4n + 2n2 Solving nT = -4n + 2n2 Solving for variable 'n'. Reorder the terms: 4n + nT + -2n2 = -4n + 2n2 + 4n + -2n2 Reorder the terms: 4n + nT + -2n2 = -4n + 4n + 2n2 + -2n2 Combine like terms: -4n + 4n = 0 4n + nT + -2n2 = 0 + 2n2 + -2n2 4n + nT + -2n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 4n + nT + -2n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(4 + T + -2n) = 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 + -2n)' equal to zero and attempt to solve: Simplifying 4 + T + -2n = 0 Solving 4 + T + -2n = 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 + -2n = 0 + -4 Reorder the terms: 4 + -4 + T + -2n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + T + -2n = 0 + -4 T + -2n = 0 + -4 Combine like terms: 0 + -4 = -4 T + -2n = -4 Add '-1T' to each side of the equation. T + -1T + -2n = -4 + -1T Combine like terms: T + -1T = 0 0 + -2n = -4 + -1T -2n = -4 + -1T Divide each side by '-2'. n = 2 + 0.5T Simplifying n = 2 + 0.5TSolution
n = {0, 2 + 0.5T}
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