3x^3=4x(2x-1)

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Solution for 3x^3=4x(2x-1) equation: 


Simplifying
3x3 = 4x(2x + -1)

Reorder the terms:
3x3 = 4x(-1 + 2x)
3x3 = (-1 * 4x + 2x * 4x)
3x3 = (-4x + 8x2)

Solving
3x3 = -4x + 8x2

Solving for variable 'x'.

Reorder the terms:
4x + -8x2 + 3x3 = -4x + 8x2 + 4x + -8x2

Reorder the terms:
4x + -8x2 + 3x3 = -4x + 4x + 8x2 + -8x2

Combine like terms: -4x + 4x = 0
4x + -8x2 + 3x3 = 0 + 8x2 + -8x2
4x + -8x2 + 3x3 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
4x + -8x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + -8x + 3x2) = 0

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


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 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 0.6666666667, 2}

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