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Simplifying (5n + -2n3) + (6n + 4n) = 0 Remove parenthesis around (5n + -2n3) 5n + -2n3 + (6n + 4n) = 0 Combine like terms: 6n + 4n = 10n 5n + -2n3 + (10n) = 0 5n + -2n3 + (10n) = 0 Reorder the terms: 5n + (10n) + -2n3 = 0 Combine like terms: 5n + (10n) = 15n 15n + -2n3 = 0 Solving 15n + -2n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(15 + -2n2) = 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 '(15 + -2n2)' equal to zero and attempt to solve: Simplifying 15 + -2n2 = 0 Solving 15 + -2n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2n2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2n2 = 0 + -15 -2n2 = 0 + -15 Combine like terms: 0 + -15 = -15 -2n2 = -15 Divide each side by '-2'. n2 = 7.5 Simplifying n2 = 7.5 Take the square root of each side: n = {-2.738612788, 2.738612788}Solution
n = {0, -2.738612788, 2.738612788}
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