5x^4-28x^2+32=0

Solution for 5x^4-28x^2+32=0 equation:

Simplifying
5x4 + -28x2 + 32 = 0

Reorder the terms:
32 + -28x2 + 5x4 = 0

Solving
32 + -28x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -5x2)(4 + -1x2) = 0

Factor a difference between two squares.
(8 + -5x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(8 + -5x2)' equal to zero and attempt to solve:

Simplifying
8 + -5x2 = 0

Solving
8 + -5x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x2 = 0 + -8
-5x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-5x2 = -8

Divide each side by '-5'.
x2 = 1.6

Simplifying
x2 = 1.6

Take the square root of each side:
x = {-1.264911064, 1.264911064}
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 = {-1.264911064, 1.264911064, -2, 2}