x^4+432=57x^2

Solution for x^4+432=57x^2 equation:

Simplifying
x4 + 432 = 57x2

Reorder the terms:
432 + x4 = 57x2

Solving
432 + x4 = 57x2

Solving for variable 'x'.

Reorder the terms:
432 + -57x2 + x4 = 57x2 + -57x2

Combine like terms: 57x2 + -57x2 = 0
432 + -57x2 + x4 = 0

Factor a trinomial.
(9 + -1x2)(48 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(48 + -1x2) = 0

Subproblem 1
Set the factor '(48 + -1x2)' equal to zero and attempt to solve:

Simplifying
48 + -1x2 = 0

Solving
48 + -1x2 = 0

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

Add '-48' to each side of the equation.
48 + -48 + -1x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -1x2 = 0 + -48
-1x2 = 0 + -48

Combine like terms: 0 + -48 = -48
-1x2 = -48

Divide each side by '-1'.
x2 = 48

Simplifying
x2 = 48

Take the square root of each side:
x = {-6.92820323, 6.92820323}
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 = {-6.92820323, 6.92820323, -3, 3}