y^4-289y^2+14400=0

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Solution for y^4-289y^2+14400=0 equation: 


Simplifying
y4 + -289y2 + 14400 = 0

Reorder the terms:
14400 + -289y2 + y4 = 0

Solving
14400 + -289y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(64 + -1y2)(225 + -1y2) = 0

Factor a difference between two squares.
((8 + y)(8 + -1y))(225 + -1y2) = 0

Factor a difference between two squares.
((15 + y)(15 + -1y))(8 + y)(8 + -1y) = 0


Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8

Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8

Subproblem 3
Set the factor '(15 + y)' equal to zero and attempt to solve:

Simplifying
15 + y = 0

Solving
15 + y = 0

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

Add '-15' to each side of the equation.
15 + -15 + y = 0 + -15

Combine like terms: 15 + -15 = 0
0 + y = 0 + -15
y = 0 + -15

Combine like terms: 0 + -15 = -15
y = -15

Simplifying
y = -15

Subproblem 4
Set the factor '(15 + -1y)' equal to zero and attempt to solve:

Simplifying
15 + -1y = 0

Solving
15 + -1y = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1y = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1y = 0 + -15
-1y = 0 + -15

Combine like terms: 0 + -15 = -15
-1y = -15

Divide each side by '-1'.
y = 15

Simplifying
y = 15
Solution
y = {-8, 8, -15, 15}

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