0=12x^3-27x^2+6x

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Solution for 0=12x^3-27x^2+6x equation: 


Simplifying
0 = 12x3 + -27x2 + 6x

Reorder the terms:
0 = 6x + -27x2 + 12x3

Solving
0 = 6x + -27x2 + 12x3

Solving for variable 'x'.
Remove the zero:
-6x + 27x2 + -12x3 = 6x + -27x2 + 12x3 + -6x + 27x2 + -12x3

Reorder the terms:
-6x + 27x2 + -12x3 = 6x + -6x + -27x2 + 27x2 + 12x3 + -12x3

Combine like terms: 6x + -6x = 0
-6x + 27x2 + -12x3 = 0 + -27x2 + 27x2 + 12x3 + -12x3
-6x + 27x2 + -12x3 = -27x2 + 27x2 + 12x3 + -12x3

Combine like terms: -27x2 + 27x2 = 0
-6x + 27x2 + -12x3 = 0 + 12x3 + -12x3
-6x + 27x2 + -12x3 = 12x3 + -12x3

Combine like terms: 12x3 + -12x3 = 0
-6x + 27x2 + -12x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-2 + 9x + -4x2) = 0

Factor a trinomial.
3x((-2 + x)(1 + -4x)) = 0

Ignore the factor 3.

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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, 2, 0.25}

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