4x^4-20x^2+24=0

Solution for 4x^4-20x^2+24=0 equation:

Simplifying
4x4 + -20x2 + 24 = 0

Reorder the terms:
24 + -20x2 + 4x4 = 0

Solving
24 + -20x2 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -5x2 + x4) = 0

Factor a trinomial.
4((2 + -1x2)(3 + -1x2)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
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}
Solution
x = {-1.414213562, 1.414213562, -1.732050808, 1.732050808}