10u^3-5u=0

Solution for 10u^3-5u=0 equation:

Simplifying
10u3 + -5u = 0

Reorder the terms:
-5u + 10u3 = 0

Solving
-5u + 10u3 = 0

Solving for variable 'u'.

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

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

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(-1 + 2u2)' equal to zero and attempt to solve:

Simplifying
-1 + 2u2 = 0

Solving
-1 + 2u2 = 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 + 2u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2u2 = 0 + 1
2u2 = 0 + 1

Combine like terms: 0 + 1 = 1
2u2 = 1

Divide each side by '2'.
u2 = 0.5

Simplifying
u2 = 0.5

Take the square root of each side:
u = {-0.707106781, 0.707106781}
Solution
u = {0, -0.707106781, 0.707106781}