y^4-36y^2=-35

Solution for y^4-36y^2=-35 equation:

Simplifying
y4 + -36y2 = -35

Reorder the terms:
-36y2 + y4 = -35

Solving
-36y2 + y4 = -35

Solving for variable 'y'.

Reorder the terms:
35 + -36y2 + y4 = -35 + 35

Combine like terms: -35 + 35 = 0
35 + -36y2 + y4 = 0

Factor a trinomial.
(1 + -1y2)(35 + -1y2) = 0

Factor a difference between two squares.
((1 + y)(1 + -1y))(35 + -1y2) = 0

Subproblem 1
Set the factor '(35 + -1y2)' equal to zero and attempt to solve:

Simplifying
35 + -1y2 = 0

Solving
35 + -1y2 = 0

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

Add '-35' to each side of the equation.
35 + -35 + -1y2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1y2 = 0 + -35
-1y2 = 0 + -35

Combine like terms: 0 + -35 = -35
-1y2 = -35

Divide each side by '-1'.
y2 = 35

Simplifying
y2 = 35

Take the square root of each side:
y = {-5.916079783, 5.916079783}
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 = {-5.916079783, 5.916079783, -1, 1}