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Simplifying 10n2 + -1n3 = 25n Solving 10n2 + -1n3 = 25n Solving for variable 'n'. Reorder the terms: -25n + 10n2 + -1n3 = 25n + -25n Combine like terms: 25n + -25n = 0 -25n + 10n2 + -1n3 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-25 + 10n + -1n2) = 0 Factor a trinomial. n((-5 + n)(5 + -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 '(-5 + n)' equal to zero and attempt to solve: Simplifying -5 + n = 0 Solving -5 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + n = 0 + 5 n = 0 + 5 Combine like terms: 0 + 5 = 5 n = 5 Simplifying n = 5Subproblem 3
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {0, 5, 5}
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