4y^4=17y^2-4

Solution for 4y^4=17y^2-4 equation:

Simplifying
4y4 = 17y2 + -4

Reorder the terms:
4y4 = -4 + 17y2

Solving
4y4 = -4 + 17y2

Solving for variable 'y'.

Reorder the terms:
4 + -17y2 + 4y4 = -4 + 17y2 + 4 + -17y2

Reorder the terms:
4 + -17y2 + 4y4 = -4 + 4 + 17y2 + -17y2

Combine like terms: -4 + 4 = 0
4 + -17y2 + 4y4 = 0 + 17y2 + -17y2
4 + -17y2 + 4y4 = 17y2 + -17y2

Combine like terms: 17y2 + -17y2 = 0
4 + -17y2 + 4y4 = 0

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

Factor a difference between two squares.
((1 + 2y)(1 + -2y))(4 + -1y2) = 0

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

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

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

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

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

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Subproblem 3
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 4
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 = {-0.5, 0.5, -2, 2}