6u^4+39u^3+18u^2=0

Solution for 6u^4+39u^3+18u^2=0 equation:

Simplifying
6u4 + 39u3 + 18u2 = 0

Reorder the terms:
18u2 + 39u3 + 6u4 = 0

Solving
18u2 + 39u3 + 6u4 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3u2'.
3u2(6 + 13u + 2u2) = 0

Factor a trinomial.
3u2((6 + u)(1 + 2u)) = 0

Ignore the factor 3.
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 '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 0

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

Add '-6' to each side of the equation.
6 + -6 + u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6
Subproblem 3
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, -6, -0.5}