t^4+6t^2-7=0

Solution for t^4+6t^2-7=0 equation:

Simplifying
t4 + 6t2 + -7 = 0

Reorder the terms:
-7 + 6t2 + t4 = 0

Solving
-7 + 6t2 + t4 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -1t2)(1 + -1t2) = 0

Factor a difference between two squares.
(-7 + -1t2)((1 + t)(1 + -1t)) = 0

Subproblem 1
Set the factor '(-7 + -1t2)' equal to zero and attempt to solve:

Simplifying
-7 + -1t2 = 0

Solving
-7 + -1t2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1t2 = 0 + 7
-1t2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1t2 = 7

Divide each side by '-1'.
t2 = -7

Simplifying
t2 = -7

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

Simplifying
1 + t = 0

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

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

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Solution
t = {-1, 1}