5u^4-27u^3-18u^2=0

Solution for 5u^4-27u^3-18u^2=0 equation:

Simplifying
5u4 + -27u3 + -18u2 = 0

Reorder the terms:
-18u2 + -27u3 + 5u4 = 0

Solving
-18u2 + -27u3 + 5u4 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u2'.
u2(-18 + -27u + 5u2) = 0

Factor a trinomial.
u2((-3 + -5u)(6 + -1u)) = 0

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 '(-3 + -5u)' equal to zero and attempt to solve:

Simplifying
-3 + -5u = 0

Solving
-3 + -5u = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5u = 0 + 3
-5u = 0 + 3

Combine like terms: 0 + 3 = 3
-5u = 3

Divide each side by '-5'.
u = -0.6

Simplifying
u = -0.6
Subproblem 3
Set the factor '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 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 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Solution
u = {0, -0.6, 6}