6n^3-18n^2-420n=0

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Solution for 6n^3-18n^2-420n=0 equation:


Simplifying
6n3 + -18n2 + -420n = 0

Reorder the terms:
-420n + -18n2 + 6n3 = 0

Solving
-420n + -18n2 + 6n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6n'.
6n(-70 + -3n + n2) = 0

Factor a trinomial.
6n((-7 + -1n)(10 + -1n)) = 0

Ignore the factor 6.

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 '(-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

Subproblem 3

Set the factor '(10 + -1n)' equal to zero and attempt to solve: Simplifying 10 + -1n = 0 Solving 10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n = 0 + -10 -1n = 0 + -10 Combine like terms: 0 + -10 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10

Solution

n = {0, -7, 10}

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