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

Solution for (4u-2)(5u-1)=0 equation:

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

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

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

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

Combine like terms: -10u + -4u = -14u
(2 + -14u + 20u2) = 0

Solving
2 + -14u + 20u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -7u + 10u2) = 0

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

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

Simplifying
1 + -5u = 0

Solving
1 + -5u = 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 + -5u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5u = 0 + -1
-5u = 0 + -1

Combine like terms: 0 + -1 = -1
-5u = -1

Divide each side by '-5'.
u = 0.2

Simplifying
u = 0.2
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 = {0.2, 0.5}