y^4-17y^2+72=

Solution for y^4-17y^2+72= equation:

Simplifying
y4 + -17y2 + 72 = 0

Reorder the terms:
72 + -17y2 + y4 = 0

Solving
72 + -17y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + -1y2)(9 + -1y2) = 0

Factor a difference between two squares.
(8 + -1y2)((3 + y)(3 + -1y)) = 0

Subproblem 1
Set the factor '(8 + -1y2)' equal to zero and attempt to solve:

Simplifying
8 + -1y2 = 0

Solving
8 + -1y2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y2 = 0 + -8
-1y2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1y2 = -8

Divide each side by '-1'.
y2 = 8

Simplifying
y2 = 8

Take the square root of each side:
y = {-2.828427125, 2.828427125}
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-2.828427125, 2.828427125, -3, 3}