(4a^4-3)(2a^4-2)=0

Solution for (4a^4-3)(2a^4-2)=0 equation:

Simplifying
(4a4 + -3)(2a4 + -2) = 0

Reorder the terms:
(-3 + 4a4)(2a4 + -2) = 0

Reorder the terms:
(-3 + 4a4)(-2 + 2a4) = 0

Multiply (-3 + 4a4) * (-2 + 2a4)
(-3(-2 + 2a4) + 4a4 * (-2 + 2a4)) = 0
((-2 * -3 + 2a4 * -3) + 4a4 * (-2 + 2a4)) = 0
((6 + -6a4) + 4a4 * (-2 + 2a4)) = 0
(6 + -6a4 + (-2 * 4a4 + 2a4 * 4a4)) = 0
(6 + -6a4 + (-8a4 + 8a8)) = 0

Combine like terms: -6a4 + -8a4 = -14a4
(6 + -14a4 + 8a8) = 0

Solving
6 + -14a4 + 8a8 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -7a4 + 4a8) = 0

Factor a trinomial.
2((3 + -4a4)(1 + -1a4)) = 0

Factor a difference between two squares.
2((3 + -4a4)((1 + a2)(1 + -1a2))) = 0

Factor a difference between two squares.
2((3 + -4a4)((1 + a2)((1 + a)(1 + -1a)))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -4a4)' equal to zero and attempt to solve:

Simplifying
3 + -4a4 = 0

Solving
3 + -4a4 = 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 + -4a4 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a4 = 0 + -3
-4a4 = 0 + -3

Combine like terms: 0 + -3 = -3
-4a4 = -3

Divide each side by '-4'.
a4 = 0.75

Simplifying
a4 = 0.75

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 + a2)' equal to zero and attempt to solve:

Simplifying
1 + a2 = 0

Solving
1 + a2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + a2 = 0 + -1
a2 = 0 + -1

Combine like terms: 0 + -1 = -1
a2 = -1

Simplifying
a2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

Add '-1' to each side of the equation.
1 + -1 + a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1
Subproblem 4
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {-1, 1}