8u^3-2u^2=0

Solution for 8u^3-2u^2=0 equation:

Simplifying
8u3 + -2u2 = 0

Reorder the terms:
-2u2 + 8u3 = 0

Solving
-2u2 + 8u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u2'.
2u2(-1 + 4u) = 0

Ignore the factor 2.
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 + 4u)' equal to zero and attempt to solve:

Simplifying
-1 + 4u = 0

Solving
-1 + 4u = 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 + 4u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4u = 0 + 1
4u = 0 + 1

Combine like terms: 0 + 1 = 1
4u = 1

Divide each side by '4'.
u = 0.25

Simplifying
u = 0.25
Solution
u = {0, 0.25}