6u^4+16u^3+8u^2=0

Solution for 6u^4+16u^3+8u^2=0 equation:

Simplifying
6u4 + 16u3 + 8u2 = 0

Reorder the terms:
8u2 + 16u3 + 6u4 = 0

Solving
8u2 + 16u3 + 6u4 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u2'.
2u2(4 + 8u + 3u2) = 0

Factor a trinomial.
2u2((2 + u)(2 + 3u)) = 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 '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Subproblem 3
Set the factor '(2 + 3u)' equal to zero and attempt to solve:

Simplifying
2 + 3u = 0

Solving
2 + 3u = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3u = 0 + -2
3u = 0 + -2

Combine like terms: 0 + -2 = -2
3u = -2

Divide each side by '3'.
u = -0.6666666667

Simplifying
u = -0.6666666667
Solution
u = {0, -2, -0.6666666667}