6t^4=-t^2+5

Solution for 6t^4=-t^2+5 equation:

Simplifying
6t4 = -1t2 + 5

Reorder the terms:
6t4 = 5 + -1t2

Solving
6t4 = 5 + -1t2

Solving for variable 't'.

Reorder the terms:
-5 + t2 + 6t4 = 5 + -1t2 + -5 + t2

Reorder the terms:
-5 + t2 + 6t4 = 5 + -5 + -1t2 + t2

Combine like terms: 5 + -5 = 0
-5 + t2 + 6t4 = 0 + -1t2 + t2
-5 + t2 + 6t4 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-5 + t2 + 6t4 = 0

Factor a trinomial.
(-1 + -1t2)(5 + -6t2) = 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 '(5 + -6t2)' equal to zero and attempt to solve:

Simplifying
5 + -6t2 = 0

Solving
5 + -6t2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6t2 = 0 + -5
-6t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-6t2 = -5

Divide each side by '-6'.
t2 = 0.8333333333

Simplifying
t2 = 0.8333333333

Take the square root of each side:
t = {-0.912870929, 0.912870929}
Solution
t = {-0.912870929, 0.912870929}