14w^4-23w^2+8=0

Solution for 14w^4-23w^2+8=0 equation:

Simplifying
14w4 + -23w2 + 8 = 0

Reorder the terms:
8 + -23w2 + 14w4 = 0

Solving
8 + -23w2 + 14w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -2w2)(8 + -7w2) = 0

Subproblem 1
Set the factor '(1 + -2w2)' equal to zero and attempt to solve:

Simplifying
1 + -2w2 = 0

Solving
1 + -2w2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2w2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2w2 = 0 + -1
-2w2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2w2 = -1

Divide each side by '-2'.
w2 = 0.5

Simplifying
w2 = 0.5

Take the square root of each side:
w = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(8 + -7w2)' equal to zero and attempt to solve:

Simplifying
8 + -7w2 = 0

Solving
8 + -7w2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7w2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7w2 = 0 + -8
-7w2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7w2 = -8

Divide each side by '-7'.
w2 = 1.142857143

Simplifying
w2 = 1.142857143

Take the square root of each side:
w = {-1.069044968, 1.069044968}
Solution
w = {-0.707106781, 0.707106781, -1.069044968, 1.069044968}