y^8-9y^5+18y^2=0

Solution for y^8-9y^5+18y^2=0 equation:

Simplifying
y8 + -9y5 + 18y2 = 0

Reorder the terms:
18y2 + -9y5 + y8 = 0

Solving
18y2 + -9y5 + y8 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(18 + -9y3 + y6) = 0

Factor a trinomial.
y2((3 + -1y3)(6 + -1y3)) = 0

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 '(3 + -1y3)' equal to zero and attempt to solve:

Simplifying
3 + -1y3 = 0

Solving
3 + -1y3 = 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 + -1y3 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y3 = 0 + -3
-1y3 = 0 + -3

Combine like terms: 0 + -3 = -3
-1y3 = -3

Divide each side by '-1'.
y3 = 3

Simplifying
y3 = 3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(6 + -1y3)' equal to zero and attempt to solve:

Simplifying
6 + -1y3 = 0

Solving
6 + -1y3 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y3 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y3 = 0 + -6
-1y3 = 0 + -6

Combine like terms: 0 + -6 = -6
-1y3 = -6

Divide each side by '-1'.
y3 = 6

Simplifying
y3 = 6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}