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

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


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

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

Reorder the terms for easier multiplication:
2x(-2 + X) = (x + 1) * 2x
(-2 * 2x + X * 2x) = (x + 1) * 2x
(-4x + 2xX) = (x + 1) * 2x

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

Reorder the terms for easier multiplication:
-4x + 2xX = 2x(1 + x)
-4x + 2xX = (1 * 2x + x * 2x)
-4x + 2xX = (2x + 2x2)

Solving
-4x + 2xX = 2x + 2x2

Solving for variable 'x'.

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

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

Reorder the terms:
-6x + 2xX + -2x2 = 2x + -2x + 2x2 + -2x2

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

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + X + -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 '(-3 + X + -1x)' equal to zero and attempt to solve: Simplifying -3 + X + -1x = 0 Solving -3 + X + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + X + 3 + -1x = 0 + 3 Reorder the terms: -3 + 3 + X + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + X + -1x = 0 + 3 X + -1x = 0 + 3 Combine like terms: 0 + 3 = 3 X + -1x = 3 Add '-1X' to each side of the equation. X + -1X + -1x = 3 + -1X Combine like terms: X + -1X = 0 0 + -1x = 3 + -1X -1x = 3 + -1X Divide each side by '-1'. x = -3 + X Simplifying x = -3 + X

Solution

x = {0, -3 + X}

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