b^4-31b^2+150=0

Solution for b^4-31b^2+150=0 equation:

Simplifying
b4 + -31b2 + 150 = 0

Reorder the terms:
150 + -31b2 + b4 = 0

Solving
150 + -31b2 + b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(6 + -1b2)(25 + -1b2) = 0

Factor a difference between two squares.
(6 + -1b2)((5 + b)(5 + -1b)) = 0

Subproblem 1
Set the factor '(6 + -1b2)' equal to zero and attempt to solve:

Simplifying
6 + -1b2 = 0

Solving
6 + -1b2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b2 = 0 + -6
-1b2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1b2 = -6

Divide each side by '-1'.
b2 = 6

Simplifying
b2 = 6

Take the square root of each side:
b = {-2.449489743, 2.449489743}
Subproblem 2
Set the factor '(5 + b)' equal to zero and attempt to solve:

Simplifying
5 + b = 0

Solving
5 + b = 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 + b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + b = 0 + -5
b = 0 + -5

Combine like terms: 0 + -5 = -5
b = -5

Simplifying
b = -5
Subproblem 3
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {-2.449489743, 2.449489743, -5, 5}