9n^3-27n^2-252n=0

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Solution for 9n^3-27n^2-252n=0 equation:


Simplifying
9n3 + -27n2 + -252n = 0

Reorder the terms:
-252n + -27n2 + 9n3 = 0

Solving
-252n + -27n2 + 9n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '9n'.
9n(-28 + -3n + n2) = 0

Factor a trinomial.
9n((-4 + -1n)(7 + -1n)) = 0

Ignore the factor 9.

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 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 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 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4

Subproblem 3

Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7

Solution

n = {0, -4, 7}

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