(1-u)(5u-2)=0

Solution for (1-u)(5u-2)=0 equation:

Simplifying
(1 + -1u)(5u + -2) = 0

Reorder the terms:
(1 + -1u)(-2 + 5u) = 0

Multiply (1 + -1u) * (-2 + 5u)
(1(-2 + 5u) + -1u * (-2 + 5u)) = 0
((-2 * 1 + 5u * 1) + -1u * (-2 + 5u)) = 0
((-2 + 5u) + -1u * (-2 + 5u)) = 0
(-2 + 5u + (-2 * -1u + 5u * -1u)) = 0
(-2 + 5u + (2u + -5u2)) = 0

Combine like terms: 5u + 2u = 7u
(-2 + 7u + -5u2) = 0

Solving
-2 + 7u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + u)(2 + -5u) = 0

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 '(2 + -5u)' equal to zero and attempt to solve:

Simplifying
2 + -5u = 0

Solving
2 + -5u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5u = 0 + -2
-5u = 0 + -2

Combine like terms: 0 + -2 = -2
-5u = -2

Divide each side by '-5'.
u = 0.4

Simplifying
u = 0.4
Solution
u = {1, 0.4}