(a^2-6)(a^2+6)=

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

Simplifying
(a2 + -6)(a2 + 6) = 0

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

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

Multiply (-6 + a2) * (6 + a2)
(-6(6 + a2) + a2(6 + a2)) = 0
((6 * -6 + a2 * -6) + a2(6 + a2)) = 0
((-36 + -6a2) + a2(6 + a2)) = 0
(-36 + -6a2 + (6 * a2 + a2 * a2)) = 0
(-36 + -6a2 + (6a2 + a4)) = 0

Combine like terms: -6a2 + 6a2 = 0
(-36 + 0 + a4) = 0
(-36 + a4) = 0

Solving
-36 + a4 = 0

Solving for variable 'a'.

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

Add '36' to each side of the equation.
-36 + 36 + a4 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + a4 = 0 + 36
a4 = 0 + 36

Combine like terms: 0 + 36 = 36
a4 = 36

Simplifying
a4 = 36

Reorder the terms:
-36 + a4 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + a4 = 0

Factor a difference between two squares.
(6 + a2)(-6 + a2) = 0

Subproblem 1
Set the factor '(6 + a2)' equal to zero and attempt to solve:

Simplifying
6 + a2 = 0

Solving
6 + a2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a2 = 0 + -6
a2 = 0 + -6

Combine like terms: 0 + -6 = -6
a2 = -6

Simplifying
a2 = -6

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 '(-6 + a2)' equal to zero and attempt to solve:

Simplifying
-6 + a2 = 0

Solving
-6 + a2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + a2 = 0 + 6
a2 = 0 + 6

Combine like terms: 0 + 6 = 6
a2 = 6

Simplifying
a2 = 6

Take the square root of each side:
a = {-2.449489743, 2.449489743}
Solution
a = {-2.449489743, 2.449489743}