4b^4-30b^2=54

Solution for 4b^4-30b^2=54 equation:

Simplifying
4b4 + -30b2 = 54

Reorder the terms:
-30b2 + 4b4 = 54

Solving
-30b2 + 4b4 = 54

Solving for variable 'b'.

Reorder the terms:
-54 + -30b2 + 4b4 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -30b2 + 4b4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -15b2 + 2b4) = 0

Factor a trinomial.
2((-3 + -2b2)(9 + -1b2)) = 0

Factor a difference between two squares.
2((-3 + -2b2)((3 + b)(3 + -1b))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -2b2)' equal to zero and attempt to solve:

Simplifying
-3 + -2b2 = 0

Solving
-3 + -2b2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2b2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2b2 = 0 + 3
-2b2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2b2 = 3

Divide each side by '-2'.
b2 = -1.5

Simplifying
b2 = -1.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

Solving
3 + b = 0

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

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

Combine like terms: 3 + -3 = 0
0 + b = 0 + -3
b = 0 + -3

Combine like terms: 0 + -3 = -3
b = -3

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

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-3, 3}