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Simplifying n2 + 21n = 2n2 + 3n Reorder the terms: 21n + n2 = 2n2 + 3n Reorder the terms: 21n + n2 = 3n + 2n2 Solving 21n + n2 = 3n + 2n2 Solving for variable 'n'. Reorder the terms: 21n + -3n + n2 + -2n2 = 3n + 2n2 + -3n + -2n2 Combine like terms: 21n + -3n = 18n 18n + n2 + -2n2 = 3n + 2n2 + -3n + -2n2 Combine like terms: n2 + -2n2 = -1n2 18n + -1n2 = 3n + 2n2 + -3n + -2n2 Reorder the terms: 18n + -1n2 = 3n + -3n + 2n2 + -2n2 Combine like terms: 3n + -3n = 0 18n + -1n2 = 0 + 2n2 + -2n2 18n + -1n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 18n + -1n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(18 + -1n) = 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 '(18 + -1n)' equal to zero and attempt to solve: Simplifying 18 + -1n = 0 Solving 18 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1n = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1n = 0 + -18 -1n = 0 + -18 Combine like terms: 0 + -18 = -18 -1n = -18 Divide each side by '-1'. n = 18 Simplifying n = 18Solution
n = {0, 18}
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