42a^4+a^2-1=

Solution for 42a^4+a^2-1= equation:

Simplifying
42a4 + a2 + -1 = 0

Reorder the terms:
-1 + a2 + 42a4 = 0

Solving
-1 + a2 + 42a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -6a2)(1 + -7a2) = 0

Subproblem 1
Set the factor '(-1 + -6a2)' equal to zero and attempt to solve:

Simplifying
-1 + -6a2 = 0

Solving
-1 + -6a2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -6a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6a2 = 0 + 1
-6a2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6a2 = 1

Divide each side by '-6'.
a2 = -0.1666666667

Simplifying
a2 = -0.1666666667

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 + -7a2)' equal to zero and attempt to solve:

Simplifying
1 + -7a2 = 0

Solving
1 + -7a2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7a2 = 0 + -1
-7a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-7a2 = -1

Divide each side by '-7'.
a2 = 0.1428571429

Simplifying
a2 = 0.1428571429

Take the square root of each side:
a = {-0.377964473, 0.377964473}
Solution
a = {-0.377964473, 0.377964473}