3y^4=28y^2-9

Solution for 3y^4=28y^2-9 equation:

Simplifying
3y4 = 28y2 + -9

Reorder the terms:
3y4 = -9 + 28y2

Solving
3y4 = -9 + 28y2

Solving for variable 'y'.

Reorder the terms:
9 + -28y2 + 3y4 = -9 + 28y2 + 9 + -28y2

Reorder the terms:
9 + -28y2 + 3y4 = -9 + 9 + 28y2 + -28y2

Combine like terms: -9 + 9 = 0
9 + -28y2 + 3y4 = 0 + 28y2 + -28y2
9 + -28y2 + 3y4 = 28y2 + -28y2

Combine like terms: 28y2 + -28y2 = 0
9 + -28y2 + 3y4 = 0

Factor a trinomial.
(1 + -3y2)(9 + -1y2) = 0

Factor a difference between two squares.
(1 + -3y2)((3 + y)(3 + -1y)) = 0

Subproblem 1
Set the factor '(1 + -3y2)' equal to zero and attempt to solve:

Simplifying
1 + -3y2 = 0

Solving
1 + -3y2 = 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 + -3y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y2 = 0 + -1
-3y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3y2 = -1

Divide each side by '-3'.
y2 = 0.3333333333

Simplifying
y2 = 0.3333333333

Take the square root of each side:
y = {-0.577350269, 0.577350269}
Subproblem 2
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 3
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 = {-0.577350269, 0.577350269, -3, 3}