2x^4-78x^2=-216

Solution for 2x^4-78x^2=-216 equation:

Simplifying
2x4 + -78x2 = -216

Reorder the terms:
-78x2 + 2x4 = -216

Solving
-78x2 + 2x4 = -216

Solving for variable 'x'.

Reorder the terms:
216 + -78x2 + 2x4 = -216 + 216

Combine like terms: -216 + 216 = 0
216 + -78x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(108 + -39x2 + x4) = 0

Factor a trinomial.
2((3 + -1x2)(36 + -1x2)) = 0

Factor a difference between two squares.
2((3 + -1x2)((6 + x)(6 + -1x))) = 0

Ignore the factor 2.
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 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

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

Simplifying
x = 6
Solution
x = {-1.732050808, 1.732050808, -6, 6}