x(x+1)=2x

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Solution for x(x+1)=2x equation:


Simplifying
x(x + 1) = 2x

Reorder the terms:
x(1 + x) = 2x
(1 * x + x * x) = 2x
(1x + x2) = 2x

Solving
1x + x2 = 2x

Solving for variable 'x'.

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

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

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

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