18y^4-21y^2+3=0

Solution for 18y^4-21y^2+3=0 equation:

Simplifying
18y4 + -21y2 + 3 = 0

Reorder the terms:
3 + -21y2 + 18y4 = 0

Solving
3 + -21y2 + 18y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -7y2 + 6y4) = 0

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

Factor a difference between two squares.
3((1 + -6y2)((1 + y)(1 + -1y))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -6y2)' equal to zero and attempt to solve:

Simplifying
1 + -6y2 = 0

Solving
1 + -6y2 = 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 + -6y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6y2 = 0 + -1
-6y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6y2 = -1

Divide each side by '-6'.
y2 = 0.1666666667

Simplifying
y2 = 0.1666666667

Take the square root of each side:
y = {-0.408248291, 0.408248291}
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 = {-0.408248291, 0.408248291, -1, 1}