x=2x+x^2

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


Simplifying
x = 2x + x2

Solving
x = 2x + x2

Solving for variable 'x'.

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

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

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

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

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

Ignore the factor -1.

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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {0, -1}

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