(6y^4)+(5y^2)-(6)=0

Solution for (6y^4)+(5y^2)-(6)=0 equation:

Simplifying
(6y4) + (5y2) + -1(6) = 0

Multiply -1 * 6
(6y4) + (5y2) + -6 = 0

Reorder the terms:
-6 + (5y2) + (6y4) = 0

Solving
-6 + (5y2) + (6y4) = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -2y2)(2 + -3y2) = 0

Subproblem 1
Set the factor '(-3 + -2y2)' equal to zero and attempt to solve:

Simplifying
-3 + -2y2 = 0

Solving
-3 + -2y2 = 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 + -2y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y2 = 0 + 3
-2y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2y2 = 3

Divide each side by '-2'.
y2 = -1.5

Simplifying
y2 = -1.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + -3y2)' equal to zero and attempt to solve:

Simplifying
2 + -3y2 = 0

Solving
2 + -3y2 = 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 + -3y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3y2 = 0 + -2
-3y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3y2 = -2

Divide each side by '-3'.
y2 = 0.6666666667

Simplifying
y2 = 0.6666666667

Take the square root of each side:
y = {-0.816496581, 0.816496581}
Solution
y = {-0.816496581, 0.816496581}