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

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

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

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

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

Solving
x2 = 1 + -1x2

Solving for variable 'x'.

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

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

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

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

Divide each side by '2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}