5x^4-41x^2-36=0

Solution for 5x^4-41x^2-36=0 equation:

Simplifying
5x4 + -41x2 + -36 = 0

Reorder the terms:
-36 + -41x2 + 5x4 = 0

Solving
-36 + -41x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -5x2)(9 + -1x2) = 0

Factor a difference between two squares.
(-4 + -5x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(-4 + -5x2)' equal to zero and attempt to solve:

Simplifying
-4 + -5x2 = 0

Solving
-4 + -5x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x2 = 0 + 4
-5x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-5x2 = 4

Divide each side by '-5'.
x2 = -0.8

Simplifying
x2 = -0.8

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

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

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