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

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


Simplifying
2x(x + -1) + -1x2 = (1 + x) * x

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

Combine like terms: 2x2 + -1x2 = 1x2
-2x + 1x2 = (1 + x) * x

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Ignore the factor -3.

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

Solution

x = {0}

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