y^4-19y^2=-60

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Solution for y^4-19y^2=-60 equation: 


Simplifying
y4 + -19y2 = -60

Reorder the terms:
-19y2 + y4 = -60

Solving
-19y2 + y4 = -60

Solving for variable 'y'.

Reorder the terms:
60 + -19y2 + y4 = -60 + 60

Combine like terms: -60 + 60 = 0
60 + -19y2 + y4 = 0

Factor a trinomial.
(4 + -1y2)(15 + -1y2) = 0

Factor a difference between two squares.
((2 + y)(2 + -1y))(15 + -1y2) = 0


Subproblem 1
Set the factor '(15 + -1y2)' equal to zero and attempt to solve:

Simplifying
15 + -1y2 = 0

Solving
15 + -1y2 = 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 + -1y2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1y2 = 0 + -15
-1y2 = 0 + -15

Combine like terms: 0 + -15 = -15
-1y2 = -15

Divide each side by '-1'.
y2 = 15

Simplifying
y2 = 15

Take the square root of each side:
y = {-3.872983346, 3.872983346}

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

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

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

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

Simplifying
y = -2

Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-3.872983346, 3.872983346, -2, 2}

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