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

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


Simplifying
x2 + -2x = x(x + -2)(x + -3)

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

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

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

Multiply (-2 + x) * (-3 + x)
-2x + x2 = x(-2(-3 + x) + x(-3 + x))
-2x + x2 = x((-3 * -2 + x * -2) + x(-3 + x))
-2x + x2 = x((6 + -2x) + x(-3 + x))
-2x + x2 = x(6 + -2x + (-3 * x + x * x))
-2x + x2 = x(6 + -2x + (-3x + x2))

Combine like terms: -2x + -3x = -5x
-2x + x2 = x(6 + -5x + x2)
-2x + x2 = (6 * x + -5x * x + x2 * x)
-2x + x2 = (6x + -5x2 + x3)

Solving
-2x + x2 = 6x + -5x2 + x3

Solving for variable 'x'.

Reorder the terms:
-2x + -6x + x2 + 5x2 + -1x3 = 6x + -5x2 + x3 + -6x + 5x2 + -1x3

Combine like terms: -2x + -6x = -8x
-8x + x2 + 5x2 + -1x3 = 6x + -5x2 + x3 + -6x + 5x2 + -1x3

Combine like terms: x2 + 5x2 = 6x2
-8x + 6x2 + -1x3 = 6x + -5x2 + x3 + -6x + 5x2 + -1x3

Reorder the terms:
-8x + 6x2 + -1x3 = 6x + -6x + -5x2 + 5x2 + x3 + -1x3

Combine like terms: 6x + -6x = 0
-8x + 6x2 + -1x3 = 0 + -5x2 + 5x2 + x3 + -1x3
-8x + 6x2 + -1x3 = -5x2 + 5x2 + x3 + -1x3

Combine like terms: -5x2 + 5x2 = 0
-8x + 6x2 + -1x3 = 0 + x3 + -1x3
-8x + 6x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-8x + 6x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 6x + -1x2) = 0

Factor a trinomial.
x((-4 + x)(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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4

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, 4, 2}

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