y^4=16y^2-48

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Solution for y^4=16y^2-48 equation: 


Simplifying
y4 = 16y2 + -48

Reorder the terms:
y4 = -48 + 16y2

Solving
y4 = -48 + 16y2

Solving for variable 'y'.

Reorder the terms:
48 + -16y2 + y4 = -48 + 16y2 + 48 + -16y2

Reorder the terms:
48 + -16y2 + y4 = -48 + 48 + 16y2 + -16y2

Combine like terms: -48 + 48 = 0
48 + -16y2 + y4 = 0 + 16y2 + -16y2
48 + -16y2 + y4 = 16y2 + -16y2

Combine like terms: 16y2 + -16y2 = 0
48 + -16y2 + y4 = 0

Factor a trinomial.
(4 + -1y2)(12 + -1y2) = 0

Factor a difference between two squares.
((2 + y)(2 + -1y))(12 + -1y2) = 0


Subproblem 1
Set the factor '(12 + -1y2)' equal to zero and attempt to solve:

Simplifying
12 + -1y2 = 0

Solving
12 + -1y2 = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1y2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1y2 = 0 + -12
-1y2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1y2 = -12

Divide each side by '-1'.
y2 = 12

Simplifying
y2 = 12

Take the square root of each side:
y = {-3.464101615, 3.464101615}

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 = {-3.464101615, 3.464101615, -2, 2}

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