2*b^4-3*b^2+1=0

Solution for 2*b^4-3*b^2+1=0 equation:

Simplifying
2b4 + -3b2 + 1 = 0

Reorder the terms:
1 + -3b2 + 2b4 = 0

Solving
1 + -3b2 + 2b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -2b2)(1 + -1b2) = 0

Factor a difference between two squares.
(1 + -2b2)((1 + b)(1 + -1b)) = 0

Subproblem 1
Set the factor '(1 + -2b2)' equal to zero and attempt to solve:

Simplifying
1 + -2b2 = 0

Solving
1 + -2b2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2b2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2b2 = 0 + -1
-2b2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2b2 = -1

Divide each side by '-2'.
b2 = 0.5

Simplifying
b2 = 0.5

Take the square root of each side:
b = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(1 + b)' equal to zero and attempt to solve:

Simplifying
1 + b = 0

Solving
1 + b = 0

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

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

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

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

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

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

Simplifying
b = 1
Solution
b = {-0.707106781, 0.707106781, -1, 1}