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

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


Simplifying
(x + -2) * x + (2 + -1x) * 3x = 0

Reorder the terms:
(-2 + x) * x + (2 + -1x) * 3x = 0

Reorder the terms for easier multiplication:
x(-2 + x) + (2 + -1x) * 3x = 0
(-2 * x + x * x) + (2 + -1x) * 3x = 0
(-2x + x2) + (2 + -1x) * 3x = 0

Reorder the terms for easier multiplication:
-2x + x2 + 3x(2 + -1x) = 0
-2x + x2 + (2 * 3x + -1x * 3x) = 0
-2x + x2 + (6x + -3x2) = 0

Reorder the terms:
-2x + 6x + x2 + -3x2 = 0

Combine like terms: -2x + 6x = 4x
4x + x2 + -3x2 = 0

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

Solving
4x + -2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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 + -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, 2}

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