6x^4+29x^2-42=0

Solution for 6x^4+29x^2-42=0 equation:

Simplifying
6x4 + 29x2 + -42 = 0

Reorder the terms:
-42 + 29x2 + 6x4 = 0

Solving
-42 + 29x2 + 6x4 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(-6 + -1x2)' equal to zero and attempt to solve:

Simplifying
-6 + -1x2 = 0

Solving
-6 + -1x2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x2 = 0 + 6

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

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

Divide each side by '-1'.
x2 = -6

Simplifying
x2 = -6

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 + -6x2)' equal to zero and attempt to solve:

Simplifying
7 + -6x2 = 0

Solving
7 + -6x2 = 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 + -6x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x2 = 0 + -7
-6x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6x2 = -7

Divide each side by '-6'.
x2 = 1.166666667

Simplifying
x2 = 1.166666667

Take the square root of each side:
x = {-1.08012345, 1.08012345}
Solution
x = {-1.08012345, 1.08012345}