=x^4+3x^2-18

Solution for =x^4+3x^2-18 equation:

Simplifying
0 = x4 + 3x2 + -18

Reorder the terms:
0 = -18 + 3x2 + x4

Solving
0 = -18 + 3x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 18 = 18
18 + -3x2 + -1x4 = -18 + 3x2 + x4 + 18 + -3x2 + -1x4

Reorder the terms:
18 + -3x2 + -1x4 = -18 + 18 + 3x2 + -3x2 + x4 + -1x4

Combine like terms: -18 + 18 = 0
18 + -3x2 + -1x4 = 0 + 3x2 + -3x2 + x4 + -1x4
18 + -3x2 + -1x4 = 3x2 + -3x2 + x4 + -1x4

Combine like terms: 3x2 + -3x2 = 0
18 + -3x2 + -1x4 = 0 + x4 + -1x4
18 + -3x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
18 + -3x2 + -1x4 = 0

Factor a trinomial.
(3 + -1x2)(6 + x2) = 0

Subproblem 1
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(6 + x2)' equal to zero and attempt to solve:

Simplifying
6 + x2 = 0

Solving
6 + x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x2 = 0 + -6
x2 = 0 + -6

Combine like terms: 0 + -6 = -6
x2 = -6

Simplifying
x2 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-1.732050808, 1.732050808}