a^4-3a^2-18=0

Solution for a^4-3a^2-18=0 equation:

Simplifying
a4 + -3a2 + -18 = 0

Reorder the terms:
-18 + -3a2 + a4 = 0

Solving
-18 + -3a2 + a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a2)(6 + -1a2) = 0

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 '(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

Take the square root of each side:
a = {-2.449489743, 2.449489743}
Solution
a = {-2.449489743, 2.449489743}