2b^4-13b^2-45=0

Solution for 2b^4-13b^2-45=0 equation:

Simplifying
2b4 + -13b2 + -45 = 0

Reorder the terms:
-45 + -13b2 + 2b4 = 0

Solving
-45 + -13b2 + 2b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -2b2)(9 + -1b2) = 0

Factor a difference between two squares.
(-5 + -2b2)((3 + b)(3 + -1b)) = 0

Subproblem 1
Set the factor '(-5 + -2b2)' equal to zero and attempt to solve:

Simplifying
-5 + -2b2 = 0

Solving
-5 + -2b2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2b2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2b2 = 0 + 5
-2b2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2b2 = 5

Divide each side by '-2'.
b2 = -2.5

Simplifying
b2 = -2.5

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}