(1-u)(4u-5)=0

Solution for (1-u)(4u-5)=0 equation:

Simplifying
(1 + -1u)(4u + -5) = 0

Reorder the terms:
(1 + -1u)(-5 + 4u) = 0

Multiply (1 + -1u) * (-5 + 4u)
(1(-5 + 4u) + -1u * (-5 + 4u)) = 0
((-5 * 1 + 4u * 1) + -1u * (-5 + 4u)) = 0
((-5 + 4u) + -1u * (-5 + 4u)) = 0
(-5 + 4u + (-5 * -1u + 4u * -1u)) = 0
(-5 + 4u + (5u + -4u2)) = 0

Combine like terms: 4u + 5u = 9u
(-5 + 9u + -4u2) = 0

Solving
-5 + 9u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-5 + 4u)(1 + -1u) = 0

Subproblem 1
Set the factor '(-5 + 4u)' equal to zero and attempt to solve:

Simplifying
-5 + 4u = 0

Solving
-5 + 4u = 0

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

Add '5' to each side of the equation.
-5 + 5 + 4u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4u = 0 + 5
4u = 0 + 5

Combine like terms: 0 + 5 = 5
4u = 5

Divide each side by '4'.
u = 1.25

Simplifying
u = 1.25
Subproblem 2
Set the factor '(1 + -1u)' equal to zero and attempt to solve:

Simplifying
1 + -1u = 0

Solving
1 + -1u = 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 + -1u = 0 + -1

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

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

Divide each side by '-1'.
u = 1

Simplifying
u = 1
Solution
u = {1.25, 1}