(2y^2+6)(3y^2-1)=

Solution for (2y^2+6)(3y^2-1)= equation:

Simplifying
(2y2 + 6)(3y2 + -1) = 0

Reorder the terms:
(6 + 2y2)(3y2 + -1) = 0

Reorder the terms:
(6 + 2y2)(-1 + 3y2) = 0

Multiply (6 + 2y2) * (-1 + 3y2)
(6(-1 + 3y2) + 2y2 * (-1 + 3y2)) = 0
((-1 * 6 + 3y2 * 6) + 2y2 * (-1 + 3y2)) = 0
((-6 + 18y2) + 2y2 * (-1 + 3y2)) = 0
(-6 + 18y2 + (-1 * 2y2 + 3y2 * 2y2)) = 0
(-6 + 18y2 + (-2y2 + 6y4)) = 0

Combine like terms: 18y2 + -2y2 = 16y2
(-6 + 16y2 + 6y4) = 0

Solving
-6 + 16y2 + 6y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 8y2 + 3y4) = 0

Factor a trinomial.
2((-3 + -1y2)(1 + -3y2)) = 0

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

Simplifying
-3 + -1y2 = 0

Solving
-3 + -1y2 = 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 + -1y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y2 = 0 + 3
-1y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1y2 = 3

Divide each side by '-1'.
y2 = -3

Simplifying
y2 = -3

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 '(1 + -3y2)' equal to zero and attempt to solve:

Simplifying
1 + -3y2 = 0

Solving
1 + -3y2 = 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 + -3y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y2 = 0 + -1
-3y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3y2 = -1

Divide each side by '-3'.
y2 = 0.3333333333

Simplifying
y2 = 0.3333333333

Take the square root of each side:
y = {-0.577350269, 0.577350269}
Solution
y = {-0.577350269, 0.577350269}