b^4-7b^2+12=0

Solution for b^4-7b^2+12=0 equation:

Simplifying
b4 + -7b2 + 12 = 0

Reorder the terms:
12 + -7b2 + b4 = 0

Solving
12 + -7b2 + b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + -1b2)(4 + -1b2) = 0

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

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

Simplifying
3 + -1b2 = 0

Solving
3 + -1b2 = 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 + -1b2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b2 = 0 + -3
-1b2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1b2 = -3

Divide each side by '-1'.
b2 = 3

Simplifying
b2 = 3

Take the square root of each side:
b = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(2 + b)' equal to zero and attempt to solve:

Simplifying
2 + b = 0

Solving
2 + b = 0

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

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

Combine like terms: 2 + -2 = 0
0 + b = 0 + -2
b = 0 + -2

Combine like terms: 0 + -2 = -2
b = -2

Simplifying
b = -2
Subproblem 3
Set the factor '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

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

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

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

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {-1.732050808, 1.732050808, -2, 2}