5x^4-51x^2+54=0

Solution for 5x^4-51x^2+54=0 equation:

Simplifying
5x4 + -51x2 + 54 = 0

Reorder the terms:
54 + -51x2 + 5x4 = 0

Solving
54 + -51x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -5x2)(9 + -1x2) = 0

Factor a difference between two squares.
(6 + -5x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(6 + -5x2)' equal to zero and attempt to solve:

Simplifying
6 + -5x2 = 0

Solving
6 + -5x2 = 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 + -5x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x2 = 0 + -6
-5x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-5x2 = -6

Divide each side by '-5'.
x2 = 1.2

Simplifying
x2 = 1.2

Take the square root of each side:
x = {-1.095445115, 1.095445115}
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 = {-1.095445115, 1.095445115, -3, 3}