3x^4+48x^2-675=0

Solution for 3x^4+48x^2-675=0 equation:

Simplifying
3x4 + 48x2 + -675 = 0

Reorder the terms:
-675 + 48x2 + 3x4 = 0

Solving
-675 + 48x2 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-225 + 16x2 + x4) = 0

Factor a trinomial.
3((-25 + -1x2)(9 + -1x2)) = 0

Factor a difference between two squares.
3((-25 + -1x2)((3 + x)(3 + -1x))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-25 + -1x2)' equal to zero and attempt to solve:

Simplifying
-25 + -1x2 = 0

Solving
-25 + -1x2 = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1x2 = 0 + 25
-1x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1x2 = 25

Divide each side by '-1'.
x2 = -25

Simplifying
x2 = -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 '(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 = {-3, 3}