7(x^4)-23(x^2)+6=0

Solution for 7(x^4)-23(x^2)+6=0 equation:

Simplifying
7(x4) + -23(x2) + 6 = 0

Reorder the terms:
6 + -23x2 + 7x4 = 0

Solving
6 + -23x2 + 7x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -7x2)(3 + -1x2) = 0

Subproblem 1
Set the factor '(2 + -7x2)' equal to zero and attempt to solve:

Simplifying
2 + -7x2 = 0

Solving
2 + -7x2 = 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 + -7x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x2 = 0 + -2
-7x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7x2 = -2

Divide each side by '-7'.
x2 = 0.2857142857

Simplifying
x2 = 0.2857142857

Take the square root of each side:
x = {-0.534522484, 0.534522484}
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 = {-0.534522484, 0.534522484, -1.732050808, 1.732050808}