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

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

Simplifying
-15x4 + 18x2 + -4 = 0

Reorder the terms:
-4 + 18x2 + -15x4 = 0

Solving
-4 + 18x2 + -15x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
0.2666666667 + -1.2x2 + x4 = 0

Move the constant term to the right:

Add '-0.2666666667' to each side of the equation.
0.2666666667 + -1.2x2 + -0.2666666667 + x4 = 0 + -0.2666666667

Reorder the terms:
0.2666666667 + -0.2666666667 + -1.2x2 + x4 = 0 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + -1.2x2 + x4 = 0 + -0.2666666667
-1.2x2 + x4 = 0 + -0.2666666667

Combine like terms: 0 + -0.2666666667 = -0.2666666667
-1.2x2 + x4 = -0.2666666667

The x term is -1.2x2.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x2 + 0.36 + x4 = -0.2666666667 + 0.36

Reorder the terms:
0.36 + -1.2x2 + x4 = -0.2666666667 + 0.36

Combine like terms: -0.2666666667 + 0.36 = 0.0933333333
0.36 + -1.2x2 + x4 = 0.0933333333

Factor a perfect square on the left side:
(x2 + -0.6)(x2 + -0.6) = 0.0933333333

Calculate the square root of the right side: 0.305505046

Break this problem into two subproblems by setting 
(x2 + -0.6) equal to 0.305505046 and -0.305505046.

Subproblem 1
x2 + -0.6 = 0.305505046

Simplifying
x2 + -0.6 = 0.305505046

Reorder the terms:
-0.6 + x2 = 0.305505046

Solving
-0.6 + x2 = 0.305505046

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x2 = 0.305505046 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x2 = 0.305505046 + 0.6
x2 = 0.305505046 + 0.6

Combine like terms: 0.305505046 + 0.6 = 0.905505046
x2 = 0.905505046

Simplifying
x2 = 0.905505046

Take the square root of each side:
x = {-0.951580289, 0.951580289}

Subproblem 2
x2 + -0.6 = -0.305505046

Simplifying
x2 + -0.6 = -0.305505046

Reorder the terms:
-0.6 + x2 = -0.305505046

Solving
-0.6 + x2 = -0.305505046

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x2 = -0.305505046 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x2 = -0.305505046 + 0.6
x2 = -0.305505046 + 0.6

Combine like terms: -0.305505046 + 0.6 = 0.294494954
x2 = 0.294494954

Simplifying
x2 = 0.294494954

Take the square root of each side:
x = {-0.542673893, 0.542673893}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.951580289, 0.951580289, -0.542673893, 0.542673893}