-x=2x-x^2

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Solution for -x=2x-x^2 equation:


Simplifying
-1x = 2x + -1x2

Solving
-1x = 2x + -1x2

Solving for variable 'x'.

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

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

Combine like terms: 2x + -2x = 0
-3x + x2 = 0 + -1x2 + x2
-3x + x2 = -1x2 + x2

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

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

Solution

x = {0, 3}

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