u^4-11u^2+18=0

Solution for u^4-11u^2+18=0 equation:

Simplifying
u4 + -11u2 + 18 = 0

Reorder the terms:
18 + -11u2 + u4 = 0

Solving
18 + -11u2 + u4 = 0

Solving for variable 'u'.

Factor a trinomial.
(2 + -1u2)(9 + -1u2) = 0

Factor a difference between two squares.
(2 + -1u2)((3 + u)(3 + -1u)) = 0

Subproblem 1
Set the factor '(2 + -1u2)' equal to zero and attempt to solve:

Simplifying
2 + -1u2 = 0

Solving
2 + -1u2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u2 = 0 + -2
-1u2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1u2 = -2

Divide each side by '-1'.
u2 = 2

Simplifying
u2 = 2

Take the square root of each side:
u = {-1.414213562, 1.414213562}
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 = {-1.414213562, 1.414213562, -3, 3}