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Simplifying 3n3 + 29n2 + -10n = 0 Reorder the terms: -10n + 29n2 + 3n3 = 0 Solving -10n + 29n2 + 3n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-10 + 29n + 3n2) = 0 Factor a trinomial. n((-10 + -1n)(1 + -3n)) = 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 '(-10 + -1n)' equal to zero and attempt to solve: Simplifying -10 + -1n = 0 Solving -10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1n = 0 + 10 -1n = 0 + 10 Combine like terms: 0 + 10 = 10 -1n = 10 Divide each side by '-1'. n = -10 Simplifying n = -10Subproblem 3
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {0, -10, 0.3333333333}
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