3b^4-b^2=24

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Solution for 3b^4-b^2=24 equation: 


Simplifying
3b4 + -1b2 = 24

Reorder the terms:
-1b2 + 3b4 = 24

Solving
-1b2 + 3b4 = 24

Solving for variable 'b'.

Reorder the terms:
-24 + -1b2 + 3b4 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -1b2 + 3b4 = 0

Factor a trinomial.
(-8 + -3b2)(3 + -1b2) = 0


Subproblem 1
Set the factor '(-8 + -3b2)' equal to zero and attempt to solve:

Simplifying
-8 + -3b2 = 0

Solving
-8 + -3b2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3b2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3b2 = 0 + 8
-3b2 = 0 + 8

Combine like terms: 0 + 8 = 8
-3b2 = 8

Divide each side by '-3'.
b2 = -2.666666667

Simplifying
b2 = -2.666666667

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 + -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}
Solution
b = {-1.732050808, 1.732050808}

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