-25t^4+10t^2+3=0

Solution for -25t^4+10t^2+3=0 equation:

Simplifying
-25t4 + 10t2 + 3 = 0

Reorder the terms:
3 + 10t2 + -25t4 = 0

Solving
3 + 10t2 + -25t4 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + -5t2)(1 + 5t2) = 0

Subproblem 1
Set the factor '(3 + -5t2)' equal to zero and attempt to solve:

Simplifying
3 + -5t2 = 0

Solving
3 + -5t2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5t2 = 0 + -3
-5t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5t2 = -3

Divide each side by '-5'.
t2 = 0.6

Simplifying
t2 = 0.6

Take the square root of each side:
t = {-0.774596669, 0.774596669}
Subproblem 2
Set the factor '(1 + 5t2)' equal to zero and attempt to solve:

Simplifying
1 + 5t2 = 0

Solving
1 + 5t2 = 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 + 5t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5t2 = 0 + -1
5t2 = 0 + -1

Combine like terms: 0 + -1 = -1
5t2 = -1

Divide each side by '5'.
t2 = -0.2

Simplifying
t2 = -0.2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {-0.774596669, 0.774596669}