y^4-8y^2=-7

Solution for y^4-8y^2=-7 equation:

Simplifying
y4 + -8y2 = -7

Reorder the terms:
-8y2 + y4 = -7

Solving
-8y2 + y4 = -7

Solving for variable 'y'.

Reorder the terms:
7 + -8y2 + y4 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + -8y2 + y4 = 0

Factor a trinomial.
(1 + -1y2)(7 + -1y2) = 0

Factor a difference between two squares.
((1 + y)(1 + -1y))(7 + -1y2) = 0

Subproblem 1
Set the factor '(7 + -1y2)' equal to zero and attempt to solve:

Simplifying
7 + -1y2 = 0

Solving
7 + -1y2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y2 = 0 + -7
-1y2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1y2 = -7

Divide each side by '-1'.
y2 = 7

Simplifying
y2 = 7

Take the square root of each side:
y = {-2.645751311, 2.645751311}
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-2.645751311, 2.645751311, -1, 1}