5x^4-178x^2-72=0

Solution for 5x^4-178x^2-72=0 equation:

Simplifying
5x4 + -178x2 + -72 = 0

Reorder the terms:
-72 + -178x2 + 5x4 = 0

Solving
-72 + -178x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -5x2)(36 + -1x2) = 0

Factor a difference between two squares.
(-2 + -5x2)((6 + x)(6 + -1x)) = 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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 = {-6, 6}