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

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

Simplifying
8a2(6 + -3a2) = 0
(6 * 8a2 + -3a2 * 8a2) = 0
(48a2 + -24a4) = 0

Solving
48a2 + -24a4 = 0

Solving for variable 'a'.

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

Ignore the factor 24.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
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 = {0, -1.414213562, 1.414213562}