15u^5+38u^4+18u^3=0

Solution for 15u^5+38u^4+18u^3=0 equation:

Simplifying
15u5 + 38u4 + 18u3 = 0

Reorder the terms:
18u3 + 38u4 + 15u5 = 0

Solving
18u3 + 38u4 + 15u5 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u3'.
u3(18 + 38u + 15u2) = 0

Subproblem 1
Set the factor 'u3' equal to zero and attempt to solve:

Simplifying
u3 = 0

Solving
u3 = 0

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

Simplifying
u3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(18 + 38u + 15u2)' equal to zero and attempt to solve:

Simplifying
18 + 38u + 15u2 = 0

Solving
18 + 38u + 15u2 = 0

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
1.2 + 2.533333333u + u2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 2.533333333u + -1.2 + u2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 2.533333333u + u2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 2.533333333u + u2 = 0 + -1.2
2.533333333u + u2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
2.533333333u + u2 = -1.2

The u term is 2.533333333u.  Take half its coefficient (1.266666667).
Square it (1.604444445) and add it to both sides.

Add '1.604444445' to each side of the equation.
2.533333333u + 1.604444445 + u2 = -1.2 + 1.604444445

Reorder the terms:
1.604444445 + 2.533333333u + u2 = -1.2 + 1.604444445

Combine like terms: -1.2 + 1.604444445 = 0.404444445
1.604444445 + 2.533333333u + u2 = 0.404444445

Factor a perfect square on the left side:
(u + 1.266666667)(u + 1.266666667) = 0.404444445

Calculate the square root of the right side: 0.635959468

Break this problem into two subproblems by setting 
(u + 1.266666667) equal to 0.635959468 and -0.635959468.

Subproblem 1
u + 1.266666667 = 0.635959468

Simplifying
u + 1.266666667 = 0.635959468

Reorder the terms:
1.266666667 + u = 0.635959468

Solving
1.266666667 + u = 0.635959468

Solving for variable 'u'.

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

Add '-1.266666667' to each side of the equation.
1.266666667 + -1.266666667 + u = 0.635959468 + -1.266666667

Combine like terms: 1.266666667 + -1.266666667 = 0.000000000
0.000000000 + u = 0.635959468 + -1.266666667
u = 0.635959468 + -1.266666667

Combine like terms: 0.635959468 + -1.266666667 = -0.630707199
u = -0.630707199

Simplifying
u = -0.630707199

Subproblem 2
u + 1.266666667 = -0.635959468

Simplifying
u + 1.266666667 = -0.635959468

Reorder the terms:
1.266666667 + u = -0.635959468

Solving
1.266666667 + u = -0.635959468

Solving for variable 'u'.

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

Add '-1.266666667' to each side of the equation.
1.266666667 + -1.266666667 + u = -0.635959468 + -1.266666667

Combine like terms: 1.266666667 + -1.266666667 = 0.000000000
0.000000000 + u = -0.635959468 + -1.266666667
u = -0.635959468 + -1.266666667

Combine like terms: -0.635959468 + -1.266666667 = -1.902626135
u = -1.902626135

Simplifying
u = -1.902626135

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.630707199, -1.902626135}
Solution
u = {-0.630707199, -1.902626135}