(1-u)(4u-2)=0

Solution for (1-u)(4u-2)=0 equation:

Simplifying
(1 + -1u)(4u + -2) = 0

Reorder the terms:
(1 + -1u)(-2 + 4u) = 0

Multiply (1 + -1u) * (-2 + 4u)
(1(-2 + 4u) + -1u * (-2 + 4u)) = 0
((-2 * 1 + 4u * 1) + -1u * (-2 + 4u)) = 0
((-2 + 4u) + -1u * (-2 + 4u)) = 0
(-2 + 4u + (-2 * -1u + 4u * -1u)) = 0
(-2 + 4u + (2u + -4u2)) = 0

Combine like terms: 4u + 2u = 6u
(-2 + 6u + -4u2) = 0

Solving
-2 + 6u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 3u + -2u2) = 0

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

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

Simplifying
-1 + u = 0

Solving
-1 + u = 0

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

Add '1' to each side of the equation.
-1 + 1 + u = 0 + 1

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

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

Simplifying
u = 1
Subproblem 2
Set the factor '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2u = 0 + -1

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

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

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {1, 0.5}