5x^4-32x^2+48=0

Solution for 5x^4-32x^2+48=0 equation:

Simplifying
5x4 + -32x2 + 48 = 0

Reorder the terms:
48 + -32x2 + 5x4 = 0

Solving
48 + -32x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(12 + -5x2)(4 + -1x2) = 0

Factor a difference between two squares.
(12 + -5x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(12 + -5x2)' equal to zero and attempt to solve:

Simplifying
12 + -5x2 = 0

Solving
12 + -5x2 = 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 + -5x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5x2 = 0 + -12
-5x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-5x2 = -12

Divide each side by '-5'.
x2 = 2.4

Simplifying
x2 = 2.4

Take the square root of each side:
x = {-1.549193338, 1.549193338}
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.549193338, 1.549193338, -2, 2}