8x^4=6x^2-1

Solution for 8x^4=6x^2-1 equation:

Simplifying
8x4 = 6x2 + -1

Reorder the terms:
8x4 = -1 + 6x2

Solving
8x4 = -1 + 6x2

Solving for variable 'x'.

Reorder the terms:
1 + -6x2 + 8x4 = -1 + 6x2 + 1 + -6x2

Reorder the terms:
1 + -6x2 + 8x4 = -1 + 1 + 6x2 + -6x2

Combine like terms: -1 + 1 = 0
1 + -6x2 + 8x4 = 0 + 6x2 + -6x2
1 + -6x2 + 8x4 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
1 + -6x2 + 8x4 = 0

Factor a trinomial.
(1 + -4x2)(1 + -2x2) = 0

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

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

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x2 = 0 + -1

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

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

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.707106781, 0.707106781, -0.5, 0.5}