u^4-2u^2-63=0

Solution for u^4-2u^2-63=0 equation:

Simplifying
u4 + -2u2 + -63 = 0

Reorder the terms:
-63 + -2u2 + u4 = 0

Solving
-63 + -2u2 + u4 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + -1u2)(9 + -1u2) = 0

Factor a difference between two squares.
(-7 + -1u2)((3 + u)(3 + -1u)) = 0

Subproblem 1
Set the factor '(-7 + -1u2)' equal to zero and attempt to solve:

Simplifying
-7 + -1u2 = 0

Solving
-7 + -1u2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1u2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1u2 = 0 + 7
-1u2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1u2 = 7

Divide each side by '-1'.
u2 = -7

Simplifying
u2 = -7

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

Simplifying
3 + u = 0

Solving
3 + u = 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 + u = 0 + -3

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

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

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

Simplifying
3 + -1u = 0

Solving
3 + -1u = 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 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {-3, 3}