u(u^4-13u^2+63)=0

Solution for u(u^4-13u^2+63)=0 equation:

Simplifying
u(u4 + -13u2 + 63) = 0

Reorder the terms:
u(63 + -13u2 + u4) = 0
(63 * u + -13u2 * u + u4 * u) = 0
(63u + -13u3 + u5) = 0

Solving
63u + -13u3 + u5 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(63 + -13u2 + u4) = 0

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

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(63 + -13u2 + u4)' equal to zero and attempt to solve:

Simplifying
63 + -13u2 + u4 = 0

Solving
63 + -13u2 + u4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-63' to each side of the equation.
63 + -13u2 + -63 + u4 = 0 + -63

Reorder the terms:
63 + -63 + -13u2 + u4 = 0 + -63

Combine like terms: 63 + -63 = 0
0 + -13u2 + u4 = 0 + -63
-13u2 + u4 = 0 + -63

Combine like terms: 0 + -63 = -63
-13u2 + u4 = -63

The u term is -13u2.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13u2 + 42.25 + u4 = -63 + 42.25

Reorder the terms:
42.25 + -13u2 + u4 = -63 + 42.25

Combine like terms: -63 + 42.25 = -20.75
42.25 + -13u2 + u4 = -20.75

Factor a perfect square on the left side:
(u2 + -6.5)(u2 + -6.5) = -20.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
u = {0}