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

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

Simplifying
(a2 + -2)(3 + -1a2) = 0

Reorder the terms:
(-2 + a2)(3 + -1a2) = 0

Multiply (-2 + a2) * (3 + -1a2)
(-2(3 + -1a2) + a2(3 + -1a2)) = 0
((3 * -2 + -1a2 * -2) + a2(3 + -1a2)) = 0
((-6 + 2a2) + a2(3 + -1a2)) = 0
(-6 + 2a2 + (3 * a2 + -1a2 * a2)) = 0
(-6 + 2a2 + (3a2 + -1a4)) = 0

Combine like terms: 2a2 + 3a2 = 5a2
(-6 + 5a2 + -1a4) = 0

Solving
-6 + 5a2 + -1a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + a2)(2 + -1a2) = 0

Subproblem 1
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

Take the square root of each side:
a = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(2 + -1a2)' equal to zero and attempt to solve:

Simplifying
2 + -1a2 = 0

Solving
2 + -1a2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a2 = 0 + -2
-1a2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1a2 = -2

Divide each side by '-1'.
a2 = 2

Simplifying
a2 = 2

Take the square root of each side:
a = {-1.414213562, 1.414213562}
Solution
a = {-1.732050808, 1.732050808, -1.414213562, 1.414213562}