4y^4+9=15y^2

Solution for 4y^4+9=15y^2 equation:

Simplifying
4y4 + 9 = 15y2

Reorder the terms:
9 + 4y4 = 15y2

Solving
9 + 4y4 = 15y2

Solving for variable 'y'.

Reorder the terms:
9 + -15y2 + 4y4 = 15y2 + -15y2

Combine like terms: 15y2 + -15y2 = 0
9 + -15y2 + 4y4 = 0

Factor a trinomial.
(3 + -4y2)(3 + -1y2) = 0

Subproblem 1
Set the factor '(3 + -4y2)' equal to zero and attempt to solve:

Simplifying
3 + -4y2 = 0

Solving
3 + -4y2 = 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 + -4y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y2 = 0 + -3
-4y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4y2 = -3

Divide each side by '-4'.
y2 = 0.75

Simplifying
y2 = 0.75

Take the square root of each side:
y = {-0.866025404, 0.866025404}
Subproblem 2
Set the factor '(3 + -1y2)' equal to zero and attempt to solve:

Simplifying
3 + -1y2 = 0

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

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

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

Divide each side by '-1'.
y2 = 3

Simplifying
y2 = 3

Take the square root of each side:
y = {-1.732050808, 1.732050808}
Solution
y = {-0.866025404, 0.866025404, -1.732050808, 1.732050808}