20X^4-53X^2+18=0

Solution for 20X^4-53X^2+18=0 equation:

Simplifying
20X4 + -53X2 + 18 = 0

Reorder the terms:
18 + -53X2 + 20X4 = 0

Solving
18 + -53X2 + 20X4 = 0

Solving for variable 'X'.

Factor a trinomial.
(2 + -5X2)(9 + -4X2) = 0

Factor a difference between two squares.
(2 + -5X2)((3 + 2X)(3 + -2X)) = 0

Subproblem 1
Set the factor '(2 + -5X2)' equal to zero and attempt to solve:

Simplifying
2 + -5X2 = 0

Solving
2 + -5X2 = 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 + -5X2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5X2 = 0 + -2
-5X2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5X2 = -2

Divide each side by '-5'.
X2 = 0.4

Simplifying
X2 = 0.4

Take the square root of each side:
X = {-0.632455532, 0.632455532}
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 = {-0.632455532, 0.632455532, -1.5, 1.5}