2x=x(3x-2)

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Solution for 2x=x(3x-2) equation: 


Simplifying
2x = x(3x + -2)

Reorder the terms:
2x = x(-2 + 3x)
2x = (-2 * x + 3x * x)
2x = (-2x + 3x2)

Solving
2x = -2x + 3x2

Solving for variable 'x'.

Combine like terms: 2x + 2x = 4x
4x + -3x2 = -2x + 3x2 + 2x + -3x2

Reorder the terms:
4x + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
4x + -3x2 = 0 + 3x2 + -3x2
4x + -3x2 = 3x2 + -3x2

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + -3x) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, 1.333333333}

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