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

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

Simplifying
5u2(2u + -1) = 0

Reorder the terms:
5u2(-1 + 2u) = 0
(-1 * 5u2 + 2u * 5u2) = 0
(-5u2 + 10u3) = 0

Solving
-5u2 + 10u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u2'.
5u2(-1 + 2u) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'u2' equal to zero and attempt to solve:

Simplifying
u2 = 0

Solving
u2 = 0

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

Simplifying
u2 = 0

Take the square root of each side:
u = {0}
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, 0.5}