u^4-14u^2+40=0

Solution for u^4-14u^2+40=0 equation:

Simplifying
u4 + -14u2 + 40 = 0

Reorder the terms:
40 + -14u2 + u4 = 0

Solving
40 + -14u2 + u4 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + -1u2)(10 + -1u2) = 0

Factor a difference between two squares.
((2 + u)(2 + -1u))(10 + -1u2) = 0

Subproblem 1
Set the factor '(10 + -1u2)' equal to zero and attempt to solve:

Simplifying
10 + -1u2 = 0

Solving
10 + -1u2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1u2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1u2 = 0 + -10
-1u2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1u2 = -10

Divide each side by '-1'.
u2 = 10

Simplifying
u2 = 10

Take the square root of each side:
u = {-3.16227766, 3.16227766}
Subproblem 2
Set the factor '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 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 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Subproblem 3
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 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 + -1u = 0 + -2

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

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

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

Simplifying
u = 2
Solution
u = {-3.16227766, 3.16227766, -2, 2}