(4u-2)(5-u)=0

Solution for (4u-2)(5-u)=0 equation:

Simplifying
(4u + -2)(5 + -1u) = 0

Reorder the terms:
(-2 + 4u)(5 + -1u) = 0

Multiply (-2 + 4u) * (5 + -1u)
(-2(5 + -1u) + 4u * (5 + -1u)) = 0
((5 * -2 + -1u * -2) + 4u * (5 + -1u)) = 0
((-10 + 2u) + 4u * (5 + -1u)) = 0
(-10 + 2u + (5 * 4u + -1u * 4u)) = 0
(-10 + 2u + (20u + -4u2)) = 0

Combine like terms: 2u + 20u = 22u
(-10 + 22u + -4u2) = 0

Solving
-10 + 22u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 11u + -2u2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + u)' equal to zero and attempt to solve:

Simplifying
-5 + u = 0

Solving
-5 + u = 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 + u = 0 + 5

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

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

Simplifying
u = 5
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 = {5, 0.5}