2x^4-8x^2-42=0

Solution for 2x^4-8x^2-42=0 equation:

Simplifying
2x4 + -8x2 + -42 = 0

Reorder the terms:
-42 + -8x2 + 2x4 = 0

Solving
-42 + -8x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4x2 + x4) = 0

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

Ignore the factor 2.
Subproblem 1
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

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 '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x2 = 0 + -7

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

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

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
Solution
x = {-2.645751311, 2.645751311}