42x^4-x^2-1=0

Solution for 42x^4-x^2-1=0 equation:

Simplifying
42x4 + -1x2 + -1 = 0

Reorder the terms:
-1 + -1x2 + 42x4 = 0

Solving
-1 + -1x2 + 42x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -7x2)(1 + -6x2) = 0

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

Simplifying
-1 + -7x2 = 0

Solving
-1 + -7x2 = 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 + -7x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7x2 = 0 + 1
-7x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-7x2 = 1

Divide each side by '-7'.
x2 = -0.1428571429

Simplifying
x2 = -0.1428571429

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -6x2)' equal to zero and attempt to solve:

Simplifying
1 + -6x2 = 0

Solving
1 + -6x2 = 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 + -6x2 = 0 + -1

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

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

Divide each side by '-6'.
x2 = 0.1666666667

Simplifying
x2 = 0.1666666667

Take the square root of each side:
x = {-0.408248291, 0.408248291}
Solution
x = {-0.408248291, 0.408248291}