x^4-2x^2+6=3x^2

Solution for x^4-2x^2+6=3x^2 equation:

Simplifying
x4 + -2x2 + 6 = 3x2

Reorder the terms:
6 + -2x2 + x4 = 3x2

Solving
6 + -2x2 + x4 = 3x2

Solving for variable 'x'.

Reorder the terms:
6 + -2x2 + -3x2 + x4 = 3x2 + -3x2

Combine like terms: -2x2 + -3x2 = -5x2
6 + -5x2 + x4 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + -5x2 + x4 = 0

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

Subproblem 1
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}
Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

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