0=x^4-5x^2+6

Solution for 0=x^4-5x^2+6 equation:

Simplifying
0 = x4 + -5x2 + 6

Reorder the terms:
0 = 6 + -5x2 + x4

Solving
0 = 6 + -5x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + 5x2 + -1x4 = 6 + -5x2 + x4 + -6 + 5x2 + -1x4

Reorder the terms:
-6 + 5x2 + -1x4 = 6 + -6 + -5x2 + 5x2 + x4 + -1x4

Combine like terms: 6 + -6 = 0
-6 + 5x2 + -1x4 = 0 + -5x2 + 5x2 + x4 + -1x4
-6 + 5x2 + -1x4 = -5x2 + 5x2 + x4 + -1x4

Combine like terms: -5x2 + 5x2 = 0
-6 + 5x2 + -1x4 = 0 + x4 + -1x4
-6 + 5x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-6 + 5x2 + -1x4 = 0

Factor a trinomial.
(-3 + x2)(2 + -1x2) = 0

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

Simplifying
-3 + x2 = 0

Solving
-3 + x2 = 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 + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x2 = 0 + 3
x2 = 0 + 3

Combine like terms: 0 + 3 = 3
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {-1.732050808, 1.732050808, -1.414213562, 1.414213562}