0=(2x-1)(-x+-1)

Solution for 0=(2x-1)(-x+-1) equation:

Simplifying
0 = (2x + -1)(-1x + -1)

Reorder the terms:
0 = (-1 + 2x)(-1x + -1)

Reorder the terms:
0 = (-1 + 2x)(-1 + -1x)

Multiply (-1 + 2x) * (-1 + -1x)
0 = (-1(-1 + -1x) + 2x * (-1 + -1x))
0 = ((-1 * -1 + -1x * -1) + 2x * (-1 + -1x))
0 = ((1 + 1x) + 2x * (-1 + -1x))
0 = (1 + 1x + (-1 * 2x + -1x * 2x))
0 = (1 + 1x + (-2x + -2x2))

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

Solving
0 = 1 + -1x + -2x2

Solving for variable 'x'.

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

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

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-1, 0.5}