5a^2(a^2+3)=54-6a^2

Solution for 5a^2(a^2+3)=54-6a^2 equation:

Simplifying
5a2(a2 + 3) = 54 + -6a2

Reorder the terms:
5a2(3 + a2) = 54 + -6a2
(3 * 5a2 + a2 * 5a2) = 54 + -6a2
(15a2 + 5a4) = 54 + -6a2

Solving
15a2 + 5a4 = 54 + -6a2

Solving for variable 'a'.

Reorder the terms:
-54 + 15a2 + 6a2 + 5a4 = 54 + -6a2 + -54 + 6a2

Combine like terms: 15a2 + 6a2 = 21a2
-54 + 21a2 + 5a4 = 54 + -6a2 + -54 + 6a2

Reorder the terms:
-54 + 21a2 + 5a4 = 54 + -54 + -6a2 + 6a2

Combine like terms: 54 + -54 = 0
-54 + 21a2 + 5a4 = 0 + -6a2 + 6a2
-54 + 21a2 + 5a4 = -6a2 + 6a2

Combine like terms: -6a2 + 6a2 = 0
-54 + 21a2 + 5a4 = 0

Factor a trinomial.
(-6 + -1a2)(9 + -5a2) = 0

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

Simplifying
-6 + -1a2 = 0

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

Combine like terms: -6 + 6 = 0
0 + -1a2 = 0 + 6
-1a2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1a2 = 6

Divide each side by '-1'.
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 '(9 + -5a2)' equal to zero and attempt to solve:

Simplifying
9 + -5a2 = 0

Solving
9 + -5a2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5a2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5a2 = 0 + -9
-5a2 = 0 + -9

Combine like terms: 0 + -9 = -9
-5a2 = -9

Divide each side by '-5'.
a2 = 1.8

Simplifying
a2 = 1.8

Take the square root of each side:
a = {-1.341640787, 1.341640787}
Solution
a = {-1.341640787, 1.341640787}