4r^4+40r^2-44=0

Solution for 4r^4+40r^2-44=0 equation:

Simplifying
4r4 + 40r2 + -44 = 0

Reorder the terms:
-44 + 40r2 + 4r4 = 0

Solving
-44 + 40r2 + 4r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + 10r2 + r4) = 0

Factor a trinomial.
4((-11 + -1r2)(1 + -1r2)) = 0

Factor a difference between two squares.
4((-11 + -1r2)((1 + r)(1 + -1r))) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-11 + -1r2)' equal to zero and attempt to solve:

Simplifying
-11 + -1r2 = 0

Solving
-11 + -1r2 = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1r2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1r2 = 0 + 11
-1r2 = 0 + 11

Combine like terms: 0 + 11 = 11
-1r2 = 11

Divide each side by '-1'.
r2 = -11

Simplifying
r2 = -11

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

Simplifying
1 + r = 0

Solving
1 + r = 0

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

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

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

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {-1, 1}