8h^4-26h^2+15=0

Solution for 8h^4-26h^2+15=0 equation:

Simplifying
8h4 + -26h2 + 15 = 0

Reorder the terms:
15 + -26h2 + 8h4 = 0

Solving
15 + -26h2 + 8h4 = 0

Solving for variable 'h'.

Factor a trinomial.
(3 + -4h2)(5 + -2h2) = 0

Subproblem 1
Set the factor '(3 + -4h2)' equal to zero and attempt to solve:

Simplifying
3 + -4h2 = 0

Solving
3 + -4h2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4h2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4h2 = 0 + -3
-4h2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4h2 = -3

Divide each side by '-4'.
h2 = 0.75

Simplifying
h2 = 0.75

Take the square root of each side:
h = {-0.866025404, 0.866025404}
Subproblem 2
Set the factor '(5 + -2h2)' equal to zero and attempt to solve:

Simplifying
5 + -2h2 = 0

Solving
5 + -2h2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2h2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2h2 = 0 + -5
-2h2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2h2 = -5

Divide each side by '-2'.
h2 = 2.5

Simplifying
h2 = 2.5

Take the square root of each side:
h = {-1.58113883, 1.58113883}
Solution
h = {-0.866025404, 0.866025404, -1.58113883, 1.58113883}