5t^4=-2t^2+3

Solution for 5t^4=-2t^2+3 equation:

Simplifying
5t4 = -2t2 + 3

Reorder the terms:
5t4 = 3 + -2t2

Solving
5t4 = 3 + -2t2

Solving for variable 't'.

Reorder the terms:
-3 + 2t2 + 5t4 = 3 + -2t2 + -3 + 2t2

Reorder the terms:
-3 + 2t2 + 5t4 = 3 + -3 + -2t2 + 2t2

Combine like terms: 3 + -3 = 0
-3 + 2t2 + 5t4 = 0 + -2t2 + 2t2
-3 + 2t2 + 5t4 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
-3 + 2t2 + 5t4 = 0

Factor a trinomial.
(-1 + -1t2)(3 + -5t2) = 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 '(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}
Solution
t = {-0.774596669, 0.774596669}