(8-3a^2)(2a^2+6)=0

Solution for (8-3a^2)(2a^2+6)=0 equation:

Simplifying
(8 + -3a2)(2a2 + 6) = 0

Reorder the terms:
(8 + -3a2)(6 + 2a2) = 0

Multiply (8 + -3a2) * (6 + 2a2)
(8(6 + 2a2) + -3a2 * (6 + 2a2)) = 0
((6 * 8 + 2a2 * 8) + -3a2 * (6 + 2a2)) = 0
((48 + 16a2) + -3a2 * (6 + 2a2)) = 0
(48 + 16a2 + (6 * -3a2 + 2a2 * -3a2)) = 0
(48 + 16a2 + (-18a2 + -6a4)) = 0

Combine like terms: 16a2 + -18a2 = -2a2
(48 + -2a2 + -6a4) = 0

Solving
48 + -2a2 + -6a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -1a2 + -3a4) = 0

Factor a trinomial.
2((8 + -3a2)(3 + a2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -3a2)' equal to zero and attempt to solve:

Simplifying
8 + -3a2 = 0

Solving
8 + -3a2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3a2 = 0 + -8
-3a2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3a2 = -8

Divide each side by '-3'.
a2 = 2.666666667

Simplifying
a2 = 2.666666667

Take the square root of each side:
a = {-1.632993162, 1.632993162}
Subproblem 2
Set the factor '(3 + a2)' equal to zero and attempt to solve:

Simplifying
3 + a2 = 0

Solving
3 + a2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a2 = 0 + -3
a2 = 0 + -3

Combine like terms: 0 + -3 = -3
a2 = -3

Simplifying
a2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {-1.632993162, 1.632993162}