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

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


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

Reorder the terms:
(-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 + a2 + 3a4) = 0

Factor a trinomial.
2((-3 + -1a2)(8 + -3a2)) = 0

Ignore the factor 2.

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

Simplifying
-3 + -1a2 = 0

Solving
-3 + -1a2 = 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 + -1a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a2 = 0 + 3
-1a2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1a2 = 3

Divide each side by '-1'.
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.

Subproblem 2
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}
Solution
a = {-1.632993162, 1.632993162}

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