2*x+2*x(x-2)=x-1*x(x-2)

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Solution for 2*x+2*x(x-2)=x-1*x(x-2) equation: 


Simplifying
2x + 2x(x + -2) = x + -1x(x + -2)

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

Combine like terms: 2x + -4x = -2x
-2x + 2x2 = x + -1x(x + -2)

Reorder the terms:
-2x + 2x2 = x + -1x(-2 + x)
-2x + 2x2 = x + (-2 * -1x + x * -1x)
-2x + 2x2 = x + (2x + -1x2)

Combine like terms: x + 2x = 3x
-2x + 2x2 = 3x + -1x2

Solving
-2x + 2x2 = 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
-2x + -3x + 2x2 + x2 = 3x + -1x2 + -3x + x2

Combine like terms: -2x + -3x = -5x
-5x + 2x2 + x2 = 3x + -1x2 + -3x + x2

Combine like terms: 2x2 + x2 = 3x2
-5x + 3x2 = 3x + -1x2 + -3x + x2

Reorder the terms:
-5x + 3x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
-5x + 3x2 = 0 + -1x2 + x2
-5x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-5x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 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 '(-5 + 3x)' equal to zero and attempt to solve:

Simplifying
-5 + 3x = 0

Solving
-5 + 3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3x = 0 + 5
3x = 0 + 5

Combine like terms: 0 + 5 = 5
3x = 5

Divide each side by '3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, 1.666666667}

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