(1-x)*x+(1-x)=0.5

Solution for (1-x)*x+(1-x)=0.5 equation:

Simplifying
(1 + -1x) * x + (1 + -1x) = 0.5

Reorder the terms for easier multiplication:
x(1 + -1x) + (1 + -1x) = 0.5
(1 * x + -1x * x) + (1 + -1x) = 0.5
(1x + -1x2) + (1 + -1x) = 0.5

Remove parenthesis around (1 + -1x)
1x + -1x2 + 1 + -1x = 0.5

Reorder the terms:
1 + 1x + -1x + -1x2 = 0.5

Combine like terms: 1x + -1x = 0
1 + 0 + -1x2 = 0.5
1 + -1x2 = 0.5

Solving
1 + -1x2 = 0.5

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + -1x2 = 0.5 + -1

Combine like terms: 1 + -1 = 0
0 + -1x2 = 0.5 + -1
-1x2 = 0.5 + -1

Combine like terms: 0.5 + -1 = -0.5
-1x2 = -0.5

Divide each side by '-1'.
x2 = 0.5

Simplifying
x2 = 0.5

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