2b^4-33b^2+16=0

Solution for 2b^4-33b^2+16=0 equation:

Simplifying
2b4 + -33b2 + 16 = 0

Reorder the terms:
16 + -33b2 + 2b4 = 0

Solving
16 + -33b2 + 2b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -2b2)(16 + -1b2) = 0

Factor a difference between two squares.
(1 + -2b2)((4 + b)(4 + -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 '(4 + b)' equal to zero and attempt to solve:

Simplifying
4 + b = 0

Solving
4 + b = 0

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

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

Combine like terms: 4 + -4 = 0
0 + b = 0 + -4
b = 0 + -4

Combine like terms: 0 + -4 = -4
b = -4

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

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {-0.707106781, 0.707106781, -4, 4}