12x^4-59x^2+72=0

Solution for 12x^4-59x^2+72=0 equation:

Simplifying
12x4 + -59x2 + 72 = 0

Reorder the terms:
72 + -59x2 + 12x4 = 0

Solving
72 + -59x2 + 12x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -4x2)(8 + -3x2) = 0

Factor a difference between two squares.
((3 + 2x)(3 + -2x))(8 + -3x2) = 0

Subproblem 1
Set the factor '(8 + -3x2)' equal to zero and attempt to solve:

Simplifying
8 + -3x2 = 0

Solving
8 + -3x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x2 = 0 + -8
-3x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3x2 = -8

Divide each side by '-3'.
x2 = 2.666666667

Simplifying
x2 = 2.666666667

Take the square root of each side:
x = {-1.632993162, 1.632993162}
Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.632993162, 1.632993162, -1.5, 1.5}