14w^4-33w^2+18=0

Solution for 14w^4-33w^2+18=0 equation:

Simplifying
14w4 + -33w2 + 18 = 0

Reorder the terms:
18 + -33w2 + 14w4 = 0

Solving
18 + -33w2 + 14w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + -7w2)(3 + -2w2) = 0

Subproblem 1
Set the factor '(6 + -7w2)' equal to zero and attempt to solve:

Simplifying
6 + -7w2 = 0

Solving
6 + -7w2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7w2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7w2 = 0 + -6
-7w2 = 0 + -6

Combine like terms: 0 + -6 = -6
-7w2 = -6

Divide each side by '-7'.
w2 = 0.8571428571

Simplifying
w2 = 0.8571428571

Take the square root of each side:
w = {-0.9258201, 0.9258201}
Subproblem 2
Set the factor '(3 + -2w2)' equal to zero and attempt to solve:

Simplifying
3 + -2w2 = 0

Solving
3 + -2w2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2w2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w2 = 0 + -3
-2w2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2w2 = -3

Divide each side by '-2'.
w2 = 1.5

Simplifying
w2 = 1.5

Take the square root of each side:
w = {-1.224744871, 1.224744871}
Solution
w = {-0.9258201, 0.9258201, -1.224744871, 1.224744871}