t^4+6t^2=40

Solution for t^4+6t^2=40 equation:

Simplifying
t4 + 6t2 = 40

Reorder the terms:
6t2 + t4 = 40

Solving
6t2 + t4 = 40

Solving for variable 't'.

Reorder the terms:
-40 + 6t2 + t4 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 6t2 + t4 = 0

Factor a trinomial.
(-10 + -1t2)(4 + -1t2) = 0

Factor a difference between two squares.
(-10 + -1t2)((2 + t)(2 + -1t)) = 0

Subproblem 1
Set the factor '(-10 + -1t2)' equal to zero and attempt to solve:

Simplifying
-10 + -1t2 = 0

Solving
-10 + -1t2 = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1t2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1t2 = 0 + 10
-1t2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1t2 = 10

Divide each side by '-1'.
t2 = -10

Simplifying
t2 = -10

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 '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 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 + t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + t = 0 + -2
t = 0 + -2

Combine like terms: 0 + -2 = -2
t = -2

Simplifying
t = -2
Subproblem 3
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-2, 2}