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

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


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

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

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

Remove parenthesis around (2x)
1x + xX = 2x(x + -1)

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

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

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + X + -2x) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + X + -2x = 0

Solving
3 + X + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + X + -3 + -2x = 0 + -3

Reorder the terms:
3 + -3 + X + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + X + -2x = 0 + -3
X + -2x = 0 + -3

Combine like terms: 0 + -3 = -3
X + -2x = -3

Add '-1X' to each side of the equation.
X + -1X + -2x = -3 + -1X

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

Divide each side by '-2'.
x = 1.5 + 0.5X

Simplifying
x = 1.5 + 0.5X
Solution
x = {0, 1.5 + 0.5X}

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