4b^4+81b^2-8100=0

Solution for 4b^4+81b^2-8100=0 equation:

Simplifying
4b4 + 81b2 + -8100 = 0

Reorder the terms:
-8100 + 81b2 + 4b4 = 0

Solving
-8100 + 81b2 + 4b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(-225 + -4b2)(36 + -1b2) = 0

Factor a difference between two squares.
(-225 + -4b2)((6 + b)(6 + -1b)) = 0

Subproblem 1
Set the factor '(-225 + -4b2)' equal to zero and attempt to solve:

Simplifying
-225 + -4b2 = 0

Solving
-225 + -4b2 = 0

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

Add '225' to each side of the equation.
-225 + 225 + -4b2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -4b2 = 0 + 225
-4b2 = 0 + 225

Combine like terms: 0 + 225 = 225
-4b2 = 225

Divide each side by '-4'.
b2 = -56.25

Simplifying
b2 = -56.25

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 '(6 + b)' equal to zero and attempt to solve:

Simplifying
6 + b = 0

Solving
6 + b = 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 + b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + b = 0 + -6
b = 0 + -6

Combine like terms: 0 + -6 = -6
b = -6

Simplifying
b = -6
Subproblem 3
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 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 + -1b = 0 + -6

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

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

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

Simplifying
b = 6
Solution
b = {-6, 6}