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

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

Simplifying
z4 + 6z2 + -7 = 0

Reorder the terms:
-7 + 6z2 + z4 = 0

Solving
-7 + 6z2 + z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -1z2)(1 + -1z2) = 0

Factor a difference between two squares.
(-7 + -1z2)((1 + z)(1 + -1z)) = 0

Subproblem 1
Set the factor '(-7 + -1z2)' equal to zero and attempt to solve:

Simplifying
-7 + -1z2 = 0

Solving
-7 + -1z2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1z2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z2 = 0 + 7
-1z2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1z2 = 7

Divide each side by '-1'.
z2 = -7

Simplifying
z2 = -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 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

Simplifying
z = -1
Subproblem 3
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = 1

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