t^4-5t^2=-6

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

Simplifying
t4 + -5t2 = -6

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

Solving
-5t2 + t4 = -6

Solving for variable 't'.

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

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

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

Subproblem 1
Set the factor '(2 + -1t2)' equal to zero and attempt to solve:

Simplifying
2 + -1t2 = 0

Solving
2 + -1t2 = 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 + -1t2 = 0 + -2

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

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

Divide each side by '-1'.
t2 = 2

Simplifying
t2 = 2

Take the square root of each side:
t = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(3 + -1t2)' equal to zero and attempt to solve:

Simplifying
3 + -1t2 = 0

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

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

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

Divide each side by '-1'.
t2 = 3

Simplifying
t2 = 3

Take the square root of each side:
t = {-1.732050808, 1.732050808}
Solution
t = {-1.414213562, 1.414213562, -1.732050808, 1.732050808}