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

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

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

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

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

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

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

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

Solving
-2 + 2x2 = -1 + x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Divide each side by '1'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}