81r^2-10r^4+81=0

Solution for 81r^2-10r^4+81=0 equation:

Simplifying
81r2 + -10r4 + 81 = 0

Reorder the terms:
81 + 81r2 + -10r4 = 0

Solving
81 + 81r2 + -10r4 = 0

Solving for variable 'r'.

Factor a trinomial.
(9 + -1r2)(9 + 10r2) = 0

Factor a difference between two squares.
((3 + r)(3 + -1r))(9 + 10r2) = 0

Subproblem 1
Set the factor '(9 + 10r2)' equal to zero and attempt to solve:

Simplifying
9 + 10r2 = 0

Solving
9 + 10r2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + 10r2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 10r2 = 0 + -9
10r2 = 0 + -9

Combine like terms: 0 + -9 = -9
10r2 = -9

Divide each side by '10'.
r2 = -0.9

Simplifying
r2 = -0.9

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 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

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

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

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

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

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

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

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

Simplifying
r = 3
Solution
r = {-3, 3}