15x^4-30x^2+10=0

Solution for 15x^4-30x^2+10=0 equation:

Simplifying
15x4 + -30x2 + 10 = 0

Reorder the terms:
10 + -30x2 + 15x4 = 0

Solving
10 + -30x2 + 15x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -6x2 + 3x4) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + -6x2 + 3x4)' equal to zero and attempt to solve:

Simplifying
2 + -6x2 + 3x4 = 0

Solving
2 + -6x2 + 3x4 = 0

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

Divide each side by '3'.
0.6666666667 + -2x2 + x4 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -2x2 + -0.6666666667 + x4 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -2x2 + x4 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -2x2 + x4 = 0 + -0.6666666667
-2x2 + x4 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-2x2 + x4 = -0.6666666667

The x term is -2x2.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x2 + 1 + x4 = -0.6666666667 + 1

Reorder the terms:
1 + -2x2 + x4 = -0.6666666667 + 1

Combine like terms: -0.6666666667 + 1 = 0.3333333333
1 + -2x2 + x4 = 0.3333333333

Factor a perfect square on the left side:
(x2 + -1)(x2 + -1) = 0.3333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(x2 + -1) equal to 0.577350269 and -0.577350269.

Subproblem 1
x2 + -1 = 0.577350269

Simplifying
x2 + -1 = 0.577350269

Reorder the terms:
-1 + x2 = 0.577350269

Solving
-1 + x2 = 0.577350269

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x2 = 0.577350269 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = 0.577350269 + 1
x2 = 0.577350269 + 1

Combine like terms: 0.577350269 + 1 = 1.577350269
x2 = 1.577350269

Simplifying
x2 = 1.577350269

Take the square root of each side:
x = {-1.25592606, 1.25592606}

Subproblem 2
x2 + -1 = -0.577350269

Simplifying
x2 + -1 = -0.577350269

Reorder the terms:
-1 + x2 = -0.577350269

Solving
-1 + x2 = -0.577350269

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x2 = -0.577350269 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = -0.577350269 + 1
x2 = -0.577350269 + 1

Combine like terms: -0.577350269 + 1 = 0.422649731
x2 = 0.422649731

Simplifying
x2 = 0.422649731

Take the square root of each side:
x = {-0.650115167, 0.650115167}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.25592606, 1.25592606, -0.650115167, 0.650115167}
Solution
x = {-1.25592606, 1.25592606, -0.650115167, 0.650115167}