(3-x)(x-1)=(x+1)(x-1)

Solution for (3-x)(x-1)=(x+1)(x-1) equation:

Simplifying
(3 + -1x)(x + -1) = (x + 1)(x + -1)

Reorder the terms:
(3 + -1x)(-1 + x) = (x + 1)(x + -1)

Multiply (3 + -1x) * (-1 + x)
(3(-1 + x) + -1x * (-1 + x)) = (x + 1)(x + -1)
((-1 * 3 + x * 3) + -1x * (-1 + x)) = (x + 1)(x + -1)
((-3 + 3x) + -1x * (-1 + x)) = (x + 1)(x + -1)
(-3 + 3x + (-1 * -1x + x * -1x)) = (x + 1)(x + -1)
(-3 + 3x + (1x + -1x2)) = (x + 1)(x + -1)

Combine like terms: 3x + 1x = 4x
(-3 + 4x + -1x2) = (x + 1)(x + -1)

Reorder the terms:
-3 + 4x + -1x2 = (1 + x)(x + -1)

Reorder the terms:
-3 + 4x + -1x2 = (1 + x)(-1 + x)

Multiply (1 + x) * (-1 + x)
-3 + 4x + -1x2 = (1(-1 + x) + x(-1 + x))
-3 + 4x + -1x2 = ((-1 * 1 + x * 1) + x(-1 + x))
-3 + 4x + -1x2 = ((-1 + 1x) + x(-1 + x))
-3 + 4x + -1x2 = (-1 + 1x + (-1 * x + x * x))
-3 + 4x + -1x2 = (-1 + 1x + (-1x + x2))

Combine like terms: 1x + -1x = 0
-3 + 4x + -1x2 = (-1 + 0 + x2)
-3 + 4x + -1x2 = (-1 + x2)

Solving
-3 + 4x + -1x2 = -1 + x2

Solving for variable 'x'.

Reorder the terms:
-3 + 1 + 4x + -1x2 + -1x2 = -1 + x2 + 1 + -1x2

Combine like terms: -3 + 1 = -2
-2 + 4x + -1x2 + -1x2 = -1 + x2 + 1 + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
-2 + 4x + -2x2 = -1 + x2 + 1 + -1x2

Reorder the terms:
-2 + 4x + -2x2 = -1 + 1 + x2 + -1x2

Combine like terms: -1 + 1 = 0
-2 + 4x + -2x2 = 0 + x2 + -1x2
-2 + 4x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2x + -1x2) = 0

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

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
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 = {1, 1}