2w^4=5w^2-3

Solution for 2w^4=5w^2-3 equation:

Simplifying
2w4 = 5w2 + -3

Reorder the terms:
2w4 = -3 + 5w2

Solving
2w4 = -3 + 5w2

Solving for variable 'w'.

Reorder the terms:
3 + -5w2 + 2w4 = -3 + 5w2 + 3 + -5w2

Reorder the terms:
3 + -5w2 + 2w4 = -3 + 3 + 5w2 + -5w2

Combine like terms: -3 + 3 = 0
3 + -5w2 + 2w4 = 0 + 5w2 + -5w2
3 + -5w2 + 2w4 = 5w2 + -5w2

Combine like terms: 5w2 + -5w2 = 0
3 + -5w2 + 2w4 = 0

Factor a trinomial.
(1 + -1w2)(3 + -2w2) = 0

Factor a difference between two squares.
((1 + w)(1 + -1w))(3 + -2w2) = 0

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

Simplifying
1 + w = 0

Solving
1 + w = 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 + w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + w = 0 + -1
w = 0 + -1

Combine like terms: 0 + -1 = -1
w = -1

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 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 + -1w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1w = 0 + -1
-1w = 0 + -1

Combine like terms: 0 + -1 = -1
-1w = -1

Divide each side by '-1'.
w = 1

Simplifying
w = 1
Solution
w = {-1.224744871, 1.224744871, -1, 1}