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Simplifying 15n = 3n3 + -4n + 12n3 + n Reorder the terms: 15n = -4n + n + 3n3 + 12n3 Combine like terms: -4n + n = -3n 15n = -3n + 3n3 + 12n3 Combine like terms: 3n3 + 12n3 = 15n3 15n = -3n + 15n3 Solving 15n = -3n + 15n3 Solving for variable 'n'. Combine like terms: 15n + 3n = 18n 18n + -15n3 = -3n + 15n3 + 3n + -15n3 Reorder the terms: 18n + -15n3 = -3n + 3n + 15n3 + -15n3 Combine like terms: -3n + 3n = 0 18n + -15n3 = 0 + 15n3 + -15n3 18n + -15n3 = 15n3 + -15n3 Combine like terms: 15n3 + -15n3 = 0 18n + -15n3 = 0 Factor out the Greatest Common Factor (GCF), '3n'. 3n(6 + -5n2) = 0 Ignore the factor 3.Subproblem 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 '(6 + -5n2)' equal to zero and attempt to solve: Simplifying 6 + -5n2 = 0 Solving 6 + -5n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5n2 = 0 + -6 -5n2 = 0 + -6 Combine like terms: 0 + -6 = -6 -5n2 = -6 Divide each side by '-5'. n2 = 1.2 Simplifying n2 = 1.2 Take the square root of each side: n = {-1.095445115, 1.095445115}Solution
n = {0, -1.095445115, 1.095445115}
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