4x^4-575x^2-144=0

Solution for 4x^4-575x^2-144=0 equation:

Simplifying
4x4 + -575x2 + -144 = 0

Reorder the terms:
-144 + -575x2 + 4x4 = 0

Solving
-144 + -575x2 + 4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -4x2)(144 + -1x2) = 0

Factor a difference between two squares.
(-1 + -4x2)((12 + x)(12 + -1x)) = 0

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

Simplifying
-1 + -4x2 = 0

Solving
-1 + -4x2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x2 = 0 + 1
-4x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4x2 = 1

Divide each side by '-4'.
x2 = -0.25

Simplifying
x2 = -0.25

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 '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Subproblem 3
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-12, 12}