4x^4-36x^2+72=0

Solution for 4x^4-36x^2+72=0 equation:

Simplifying
4x4 + -36x2 + 72 = 0

Reorder the terms:
72 + -36x2 + 4x4 = 0

Solving
72 + -36x2 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -9x2 + x4) = 0

Factor a trinomial.
4((3 + -1x2)(6 + -1x2)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {-1.732050808, 1.732050808, -2.449489743, 2.449489743}