2y^4=11y^2-12

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Solution for 2y^4=11y^2-12 equation: 


Simplifying
2y4 = 11y2 + -12

Reorder the terms:
2y4 = -12 + 11y2

Solving
2y4 = -12 + 11y2

Solving for variable 'y'.

Reorder the terms:
12 + -11y2 + 2y4 = -12 + 11y2 + 12 + -11y2

Reorder the terms:
12 + -11y2 + 2y4 = -12 + 12 + 11y2 + -11y2

Combine like terms: -12 + 12 = 0
12 + -11y2 + 2y4 = 0 + 11y2 + -11y2
12 + -11y2 + 2y4 = 11y2 + -11y2

Combine like terms: 11y2 + -11y2 = 0
12 + -11y2 + 2y4 = 0

Factor a trinomial.
(3 + -2y2)(4 + -1y2) = 0

Factor a difference between two squares.
(3 + -2y2)((2 + y)(2 + -1y)) = 0


Subproblem 1
Set the factor '(3 + -2y2)' equal to zero and attempt to solve:

Simplifying
3 + -2y2 = 0

Solving
3 + -2y2 = 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 + -2y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y2 = 0 + -3
-2y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2y2 = -3

Divide each side by '-2'.
y2 = 1.5

Simplifying
y2 = 1.5

Take the square root of each side:
y = {-1.224744871, 1.224744871}

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 = {-1.224744871, 1.224744871, -2, 2}

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