3t^4=-t^2+2

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

Simplifying
3t4 = -1t2 + 2

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

Solving
3t4 = 2 + -1t2

Solving for variable 't'.

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

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

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

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

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

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 '(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

Take the square root of each side:
t = {-0.816496581, 0.816496581}
Solution
t = {-0.816496581, 0.816496581}