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

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

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

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

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

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

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

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

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

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

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

Add '1' to each side of the equation.
-1 + 1 + x2 = -1 + -1x + 1 + 2x2

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

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

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

Solving
x2 = -1x + 2x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 1}