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

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


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

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

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

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

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

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

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

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

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

Solving
-1 + x2 = -2 + 3x + -1x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Factor a trinomial.
(1 + -2x)(1 + -1x) = 0


Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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 = {0.5, 1}

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