2=3t^4-t^2

Solution for 2=3t^4-t^2 equation:

Simplifying
2 = 3t4 + -1t2

Reorder the terms:
2 = -1t2 + 3t4

Solving
2 = -1t2 + 3t4

Solving for variable 't'.

Reorder the terms:
2 + t2 + -3t4 = -1t2 + t2 + 3t4 + -3t4

Combine like terms: -1t2 + t2 = 0
2 + t2 + -3t4 = 0 + 3t4 + -3t4
2 + t2 + -3t4 = 3t4 + -3t4

Combine like terms: 3t4 + -3t4 = 0
2 + t2 + -3t4 = 0

Factor a trinomial.
(1 + -1t2)(2 + 3t2) = 0

Factor a difference between two squares.
((1 + t)(1 + -1t))(2 + 3t2) = 0

Subproblem 1
Set the factor '(2 + 3t2)' equal to zero and attempt to solve:

Simplifying
2 + 3t2 = 0

Solving
2 + 3t2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3t2 = 0 + -2
3t2 = 0 + -2

Combine like terms: 0 + -2 = -2
3t2 = -2

Divide each side by '3'.
t2 = -0.6666666667

Simplifying
t2 = -0.6666666667

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 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 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 + t = 0 + -1

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

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

Simplifying
t = -1
Subproblem 3
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 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 + -1t = 0 + -1

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

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

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {-1, 1}