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Simplifying 15n + 3n^{4}+ -4n + 12n^{4}+ n = 0 Reorder the terms: 15n + -4n + n + 3n^{4}+ 12n^{4}= 0 Combine like terms: 15n + -4n = 11n 11n + n + 3n^{4}+ 12n^{4}= 0 Combine like terms: 11n + n = 12n 12n + 3n^{4}+ 12n^{4}= 0 Combine like terms: 3n^{4}+ 12n^{4}= 15n^{4}12n + 15n^{4}= 0 Solving 12n + 15n^{4}= 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(4 + 5n^{3}) = 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 = 0## Subproblem 2

Set the factor '(4 + 5n^{3})' equal to zero and attempt to solve: Simplifying 4 + 5n^{3}= 0 Solving 4 + 5n^{3}= 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5n^{3}= 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5n^{3}= 0 + -4 5n^{3}= 0 + -4 Combine like terms: 0 + -4 = -4 5n^{3}= -4 Divide each side by '5'. n^{3}= -0.8 Simplifying n^{3}= -0.8 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.## Solution

n = {0}

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