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Simplifying 3n + -2n^{4}+ n + 7n^{4}+ -2n = 0 Reorder the terms: 3n + n + -2n + -2n^{4}+ 7n^{4}= 0 Combine like terms: 3n + n = 4n 4n + -2n + -2n^{4}+ 7n^{4}= 0 Combine like terms: 4n + -2n = 2n 2n + -2n^{4}+ 7n^{4}= 0 Combine like terms: -2n^{4}+ 7n^{4}= 5n^{4}2n + 5n^{4}= 0 Solving 2n + 5n^{4}= 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(2 + 5n^{3}) = 0## 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 '(2 + 5n^{3})' equal to zero and attempt to solve: Simplifying 2 + 5n^{3}= 0 Solving 2 + 5n^{3}= 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5n^{3}= 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5n^{3}= 0 + -2 5n^{3}= 0 + -2 Combine like terms: 0 + -2 = -2 5n^{3}= -2 Divide each side by '5'. n^{3}= -0.4 Simplifying n^{3}= -0.4 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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