3t^2+2=9t^4

Solution for 3t^2+2=9t^4 equation:

Simplifying
3t2 + 2 = 9t4

Reorder the terms:
2 + 3t2 = 9t4

Solving
2 + 3t2 = 9t4

Solving for variable 't'.

Combine like terms: 9t4 + -9t4 = 0
2 + 3t2 + -9t4 = 0

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

Take the square root of each side:
t = {-0.816496581, 0.816496581}
Subproblem 2
Set the factor '(1 + 3t2)' equal to zero and attempt to solve:

Simplifying
1 + 3t2 = 0

Solving
1 + 3t2 = 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 + 3t2 = 0 + -1

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

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

Divide each side by '3'.
t2 = -0.3333333333

Simplifying
t2 = -0.3333333333

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {-0.816496581, 0.816496581}