y^4+45=14y^2

Solution for y^4+45=14y^2 equation:

Simplifying
y4 + 45 = 14y2

Reorder the terms:
45 + y4 = 14y2

Solving
45 + y4 = 14y2

Solving for variable 'y'.

Reorder the terms:
45 + -14y2 + y4 = 14y2 + -14y2

Combine like terms: 14y2 + -14y2 = 0
45 + -14y2 + y4 = 0

Factor a trinomial.
(5 + -1y2)(9 + -1y2) = 0

Factor a difference between two squares.
(5 + -1y2)((3 + y)(3 + -1y)) = 0

Subproblem 1
Set the factor '(5 + -1y2)' equal to zero and attempt to solve:

Simplifying
5 + -1y2 = 0

Solving
5 + -1y2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y2 = 0 + -5
-1y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1y2 = -5

Divide each side by '-1'.
y2 = 5

Simplifying
y2 = 5

Take the square root of each side:
y = {-2.236067978, 2.236067978}
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 = {-2.236067978, 2.236067978, -3, 3}