36t^4+30t^2-6=0

Solution for 36t^4+30t^2-6=0 equation:

Simplifying
36t4 + 30t2 + -6 = 0

Reorder the terms:
-6 + 30t2 + 36t4 = 0

Solving
-6 + 30t2 + 36t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 5t2 + 6t4) = 0

Factor a trinomial.
6((-1 + -1t2)(1 + -6t2)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -1t2)' equal to zero and attempt to solve:

Simplifying
-1 + -1t2 = 0

Solving
-1 + -1t2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1t2 = 0 + 1
-1t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1t2 = 1

Divide each side by '-1'.
t2 = -1

Simplifying
t2 = -1

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 + -6t2)' equal to zero and attempt to solve:

Simplifying
1 + -6t2 = 0

Solving
1 + -6t2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6t2 = 0 + -1
-6t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6t2 = -1

Divide each side by '-6'.
t2 = 0.1666666667

Simplifying
t2 = 0.1666666667

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