6x^3=9x^2-3x

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Solution for 6x^3=9x^2-3x equation: 


Simplifying
6x3 = 9x2 + -3x

Reorder the terms:
6x3 = -3x + 9x2

Solving
6x3 = -3x + 9x2

Solving for variable 'x'.

Reorder the terms:
3x + -9x2 + 6x3 = -3x + 9x2 + 3x + -9x2

Reorder the terms:
3x + -9x2 + 6x3 = -3x + 3x + 9x2 + -9x2

Combine like terms: -3x + 3x = 0
3x + -9x2 + 6x3 = 0 + 9x2 + -9x2
3x + -9x2 + 6x3 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
3x + -9x2 + 6x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + -3x + 2x2) = 0

Factor a trinomial.
3x((1 + -2x)(1 + -1x)) = 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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 0.5, 1}

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