81n^3+36n^2=-4n

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Solution for 81n^3+36n^2=-4n equation:


Simplifying
81n3 + 36n2 = -4n

Reorder the terms:
36n2 + 81n3 = -4n

Solving
36n2 + 81n3 = -4n

Solving for variable 'n'.

Reorder the terms:
4n + 36n2 + 81n3 = -4n + 4n

Combine like terms: -4n + 4n = 0
4n + 36n2 + 81n3 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(4 + 36n + 81n2) = 0

Factor a trinomial.
n((2 + 9n)(2 + 9n)) = 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 + 9n)' equal to zero and attempt to solve: Simplifying 2 + 9n = 0 Solving 2 + 9n = 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 + 9n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9n = 0 + -2 9n = 0 + -2 Combine like terms: 0 + -2 = -2 9n = -2 Divide each side by '9'. n = -0.2222222222 Simplifying n = -0.2222222222

Subproblem 3

Set the factor '(2 + 9n)' equal to zero and attempt to solve: Simplifying 2 + 9n = 0 Solving 2 + 9n = 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 + 9n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9n = 0 + -2 9n = 0 + -2 Combine like terms: 0 + -2 = -2 9n = -2 Divide each side by '9'. n = -0.2222222222 Simplifying n = -0.2222222222

Solution

n = {0, -0.2222222222, -0.2222222222}

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