-15x^4+18x^2-3=0

Solution for -15x^4+18x^2-3=0 equation:

Simplifying
-15x4 + 18x2 + -3 = 0

Reorder the terms:
-3 + 18x2 + -15x4 = 0

Solving
-3 + 18x2 + -15x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 6x2 + -5x4) = 0

Factor a trinomial.
3((-1 + x2)(1 + -5x2)) = 0

Factor a difference between two squares.
3(((1 + x)(-1 + x))(1 + -5x2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -5x2)' equal to zero and attempt to solve:

Simplifying
1 + -5x2 = 0

Solving
1 + -5x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x2 = 0 + -1
-5x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5x2 = -1

Divide each side by '-5'.
x2 = 0.2

Simplifying
x2 = 0.2

Take the square root of each side:
x = {-0.447213596, 0.447213596}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {-0.447213596, 0.447213596, -1, 1}