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

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


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

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

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

Solving
1x + x2 = -2x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -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 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0, 3}

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