4y^4=37y^2-9

Solution for 4y^4=37y^2-9 equation:

Simplifying
4y4 = 37y2 + -9

Reorder the terms:
4y4 = -9 + 37y2

Solving
4y4 = -9 + 37y2

Solving for variable 'y'.

Reorder the terms:
9 + -37y2 + 4y4 = -9 + 37y2 + 9 + -37y2

Reorder the terms:
9 + -37y2 + 4y4 = -9 + 9 + 37y2 + -37y2

Combine like terms: -9 + 9 = 0
9 + -37y2 + 4y4 = 0 + 37y2 + -37y2
9 + -37y2 + 4y4 = 37y2 + -37y2

Combine like terms: 37y2 + -37y2 = 0
9 + -37y2 + 4y4 = 0

Factor a trinomial.
(1 + -4y2)(9 + -1y2) = 0

Factor a difference between two squares.
((1 + 2y)(1 + -2y))(9 + -1y2) = 0

Factor a difference between two squares.
((3 + y)(3 + -1y))(1 + 2y)(1 + -2y) = 0

Subproblem 1
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

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

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

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Subproblem 3
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Subproblem 4
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-0.5, 0.5, -3, 3}