0=6x^3-108x

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Solution for 0=6x^3-108x equation:


Simplifying
0 = 6x3 + -108x

Reorder the terms:
0 = -108x + 6x3

Solving
0 = -108x + 6x3

Solving for variable 'x'.
Remove the zero:
108x + -6x3 = -108x + 6x3 + 108x + -6x3

Reorder the terms:
108x + -6x3 = -108x + 108x + 6x3 + -6x3

Combine like terms: -108x + 108x = 0
108x + -6x3 = 0 + 6x3 + -6x3
108x + -6x3 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
108x + -6x3 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(18 + -1x2) = 0

Ignore the factor 6.

Subproblem 1

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

Subproblem 2

Set the factor '(18 + -1x2)' equal to zero and attempt to solve: Simplifying 18 + -1x2 = 0 Solving 18 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x2 = 0 + -18 -1x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -1x2 = -18 Divide each side by '-1'. x2 = 18 Simplifying x2 = 18 Take the square root of each side: x = {-4.242640687, 4.242640687}

Solution

x = {0, -4.242640687, 4.242640687}

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