5u^4-19u^2+12=0

Solution for 5u^4-19u^2+12=0 equation:

Simplifying
5u4 + -19u2 + 12 = 0

Reorder the terms:
12 + -19u2 + 5u4 = 0

Solving
12 + -19u2 + 5u4 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + -5u2)(3 + -1u2) = 0

Subproblem 1
Set the factor '(4 + -5u2)' equal to zero and attempt to solve:

Simplifying
4 + -5u2 = 0

Solving
4 + -5u2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5u2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5u2 = 0 + -4
-5u2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5u2 = -4

Divide each side by '-5'.
u2 = 0.8

Simplifying
u2 = 0.8

Take the square root of each side:
u = {-0.894427191, 0.894427191}
Subproblem 2
Set the factor '(3 + -1u2)' equal to zero and attempt to solve:

Simplifying
3 + -1u2 = 0

Solving
3 + -1u2 = 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 + -1u2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u2 = 0 + -3
-1u2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1u2 = -3

Divide each side by '-1'.
u2 = 3

Simplifying
u2 = 3

Take the square root of each side:
u = {-1.732050808, 1.732050808}
Solution
u = {-0.894427191, 0.894427191, -1.732050808, 1.732050808}