y^4=5y^4-4y^2

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Solution for y^4=5y^4-4y^2 equation: 


Simplifying
y4 = 5y4 + -4y2

Reorder the terms:
y4 = -4y2 + 5y4

Solving
y4 = -4y2 + 5y4

Solving for variable 'y'.

Reorder the terms:
4y2 + y4 + -5y4 = -4y2 + 5y4 + 4y2 + -5y4

Combine like terms: y4 + -5y4 = -4y4
4y2 + -4y4 = -4y2 + 5y4 + 4y2 + -5y4

Reorder the terms:
4y2 + -4y4 = -4y2 + 4y2 + 5y4 + -5y4

Combine like terms: -4y2 + 4y2 = 0
4y2 + -4y4 = 0 + 5y4 + -5y4
4y2 + -4y4 = 5y4 + -5y4

Combine like terms: 5y4 + -5y4 = 0
4y2 + -4y4 = 0

Factor out the Greatest Common Factor (GCF), '4y2'.
4y2(1 + -1y2) = 0

Factor a difference between two squares.
4y2((1 + y)(1 + -1y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {0, -1, 1}

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