6c^3+18c^2-324c=0

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Solution for 6c^3+18c^2-324c=0 equation:


Simplifying
6c3 + 18c2 + -324c = 0

Reorder the terms:
-324c + 18c2 + 6c3 = 0

Solving
-324c + 18c2 + 6c3 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '6c'.
6c(-54 + 3c + c2) = 0

Factor a trinomial.
6c((-9 + -1c)(6 + -1c)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0

Subproblem 2

Set the factor '(-9 + -1c)' equal to zero and attempt to solve: Simplifying -9 + -1c = 0 Solving -9 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1c = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1c = 0 + 9 -1c = 0 + 9 Combine like terms: 0 + 9 = 9 -1c = 9 Divide each side by '-1'. c = -9 Simplifying c = -9

Subproblem 3

Set the factor '(6 + -1c)' equal to zero and attempt to solve: Simplifying 6 + -1c = 0 Solving 6 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1c = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1c = 0 + -6 -1c = 0 + -6 Combine like terms: 0 + -6 = -6 -1c = -6 Divide each side by '-1'. c = 6 Simplifying c = 6

Solution

c = {0, -9, 6}

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